Explanation:

একটি থলিতে ৬টি নীল বল, ৪টি সাদা বল এবং ১০ টি কালো বল আছে। দৈবভাবে একটি বল তুললে সেটি সাদা না হবার সম্ভবনা কত? সঠিক উত্তর 23 মোট বলের সংখ্যা (6 + 8 + 10) বা 24 টি সাদা " " ৪ টি .০. দৈবভাবে একটি বল তুললে সেটি সাদা হবার সম্ভবনা = 824 = 13 অতএব " " " " সাদা না হবার সম্ভবনা = (1 - 13) = 23

Explanation:

There are 15 boys and 10 girls in a class. If three students are selected at random , what is the probability that 1 girl and 2 boys are selected? Correct Answer 2146 1 girl & 2 boys can be selected in = (10C1) × (15C2) ways = 10 × 105 ways = 1050 ways. 3 students can be selected from 25 students = 25C3 = 2300 ways Required probability = 1050/2300 = 21/46. Ans: C

Explanation:

12 marbles are selected at random form a large collection of white , red, green and yellow marbles . The number of marbles of each color is unlimited. Find the probability that the selection contains at least one marble of each color ? Correct Answer 3391 12 marbles are selected at random form a large collection of white , red, green and yellow marbles . The number of marbles of each color is unlimited. Find the probability that the selection contains at least one marble of each color ? This is same as W + R + G + Y = 12, where all are positive integers. Step I.. first, give one to each, hence 4 gone. Now you can distribute the remaining 8 to anyone as the restriction of at least one is done.. W + R + G + Y = 8..W + R + G + Y = 8.. Now, take this as 8 marbles and 3 partitions, so total 11 things. You can choose these 3 partitions in 11C3 ways = 11!/8!3! = 11∗10∗9/3∗2 = 11∗5∗3 Step II.. Total ways.. W + R + G + Y = 12 Now, take this as 12 marbles and 3 partitions, so total 15 things. You can choose these 3 partitions in 15C3 ways = 15!/12!3! = 15∗14∗13/3∗2 = 5∗7∗13 Probability = 11∗5∗3/5∗7∗13 = 33/91

Explanation:

what is the probability that an integer selected at random from those between 10 and 100 inclusive is a multiple of 5 or 9? Correct Answer 2791 1  -  100 পর্যন্ত  সংখ্যাগুলর মধ্যে 5 দ্বারা বিভাজ্য সংখ্যা 5)100(20                                                                                                 1000⸫ 10  -  100 পর্যন্ত  সংখ্যাগুলর মধ্যে 9 দ্বারা বিভাজ্য সংখ্যা  =  11 - 1 = 10 টিএখন 5 এবং 9 উভয় দ্বারা বিভাজ্য সংখ্যা  =  2 টি (45 এবং 90)⸫ 5 অথবা 9 দ্বারা বিভাজ্য সংখ্যা =  19 + 10 - 2 = 27⸫ সম্ভাব্যতা  =  2791

Explanation:

What is the probability that product of two integers (not necessarily different integers ) randomly selected from the numbers 1 to 20, inclusive , is odd ? Correct Answer 1/4 আমরা জানি, শুধুমাত্র দুটি বিজোড় সংখ্যার গুণফলই বিজোড় হয়। এখানে 1 থেকে 20 পর্যন্ত বিজোড় সংখ্যা 10টি এবং যেহেতু প্রশ্নে বলা হয়েছে সংখ্যা দুটি ভিন্ন নাও হতে পারে তাই সম্ভাব্যতা = 10×1020×20  =  14 ।

Explanation:

In a container , there are 2 green marbles and 2 red marbles . You randomly pick the marbles. What is the probability that both of the are green? Correct Answer 1/6 green ball = 2 Red ball = 2 From 4 balls, possibility of 2 green = 4C2 = 6 From 2 balls, possibility of 1 green = 2C2 = 1. From rest 2 balls, possibility of being green = 2C2 = 1 Possibility of 2 green = (2C2 x 2C2)/4C2 = (1×1)/6 = 1/6 Ans: 1/6

Explanation:

A box contains 10 electric bulbs from which 2 bulbs are defective . Two bulbs are chosen at random. What is the probability that one of them is defective? Correct Answer 16/45 Defective 2; Normal ৪ Probability that one of them is defective will be, = (8C1×2C2)/10C2 = (8×2)/45   = 16/45 (ans)

Explanation:

A bag contains 6 black and 8 white . One ball is drawn at random. What is the probability that the ball drawn is white ? Correct Answer 4/7 ইউরোপীয় ইউনিয়ন (ELI) ছাড়াও বেনেলাক্স, ন্যাটো, ইউরোপীয় কাউন্সিল, ACP ও বিশ্ব শুল্ক সংস্থার (WCO) সদর দপ্তর ব্রাসেলসে অবস্থিত।

Explanation:

A bag contains 4 white , 5 red and 6 blue balls. Three balls are drawn at rand dom from the bag .The probability that all of them are red.is : Correct Answer 291 Let S be the sample space Then, n(S) = number of ways of drawing 3 balls out of 15 = 15C3 = (15 × 14 × 13)/(3 × 2 × 1) = 455 Let E = event of getting all the 3 red balls ∴n(E) = 5C3 = 5C2 = (5 × 4)/(2 × 1) = 10 ∴P(E) = n(E)/n(S) = 10/455 = 291

Explanation:

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is - Correct Answer 1/9 One person can select one house out of 3 = 3C1 ways = 3. Hence, three persons can select one house out of 3 in 3 x 3 x 3 = 9. Therefore, the probability that all three apply for the same house is 1/9.

Explanation:

Three dice are thrown together . Find the probability of getting a total of at least 6 ? Correct Answer 103108 Number of events of getting a total of less than 6 (event of getting a total of 3, 4 or 5) = 10 i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1) (1, 1, 3), (1, 3, 1), (3, 1, 1), (1, 2, 2), (2, 1, 2), (2, 2, 1). Therefore, probability of getting a total of less than 6 Number of favorable outcomes P(E6) = Total number of possible outcome = 10/216 = 5/108 Therefore, probability of getting a total of at least 6 = 1 - P(getting a total of less than 6) = 1 - 5/108 = (108 - 5)/108 = 103/108 These examples will help us to solve different types of problems based on probability for rolling three dice.

Explanation:

All possible three digit numbers are formed by 1,3,5 . If one number is chosen randomly, the probability that it would be divisible by 5 is - Correct Answer 13 1,3,5 এই তিনটি অঙ্ক দ্বারা গঠিত মোট সংখ্যা = 1,3,5 অঙ্ক তিনটিকে যতভাবে বিন্যস্ত করা যায় সেই সংখ্যা = 3! 5 দ্বারা বিভাজ্য হলে, সংখ্যাটির একক স্থানীয় অঙ্ক 5 হতে হবে [∴ শূন্য (০) নেই]। ∴ 5 কে একক এর স্থানে রেখে বাকি অঙ্কদ্বয়কে সাজানোর উপায় = 5 কে একক স্থানে রেখে গঠিত মোট সংখ্যা = 2! ∴ নির্ণেয় সম্ভব্যতা = 2!3! = 2!3×2! = 13

Explanation:

A driver of an auto rickshaw sees a lorry m ahead of him .After 30 seconds the lorry 90 m behind. If the speed of the auto rickshaw is 38 km /hr, then what is the speed of the lorry? Correct Answer 20 km /hr Relative Speed  = Total distance Total time = 60 + 9030 = 15030 = 5m/s.'. 5m/s  = 5×185 = 18 km/hrNow, relative speed = speed of auto rickshaw  -  speed of lorry ⇒18 = 38 - speed of lory⇒speed of lorry  = 38 - 18 = 20 km/hr

Explanation:

A box contains 21 balls numbered 1 to 21 . A ball numbered 1 to 21 . A ball is drawn and then another ball is brawn without replacement . What is the probability that both balls are even numbered? Correct Answer 3/14 There are 10 even number in the group 1 - 21 ∴ The probability that the first ball is even numbed 1021 And the probability that the second ball is even numbered 920 ∴ Required probability = = 1021×920 = 90420 = 314

Explanation:

A bag cotains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is - Correct Answer 2/91 Given, white = 4 Red = 5 Blue = 6 Total = 15 The probability that all of them are red = C35C315 = 5!3!(5 - 3)!15!3!(15 - 3)! = 5!3!2!3!12! = 5×4×3!2×3!15×14×13×12!3×2×12! = 10455 = 291

Explanation:

A word consists of 9 letters; 5 consonants and 4 vowels. There letters are chosen at random. What is the probability that more than one vowel will be selected? Correct Answer 17/42 Given, Consonants = 5 Vowels = 4 Probability = = {1 - (C35C39 + C25×C14C39)} = {1 - (5!3!(5 - 3)!9!3!(9 - 3)! + 5!2!(5 - 2)!×4!1!(4 - 1)!9!3!(9 - 3)!)} = {1 - (5!3!2!9!3!6! + 5!2!3!×4!1!3!9!3!6!)} = {1 - (5×4×3!2×3!9×8×7×6!2×3×6! + 5×4×3!2×3!×4×3!3!9×8×7×6!2×3×6!)} = {1 - (1084 + 10×484)} = (1 - 5084) = (80 - 5084) = 3484 = 1742

Explanation:

There are 3 green , 4 orange and 5 white color bulbs in a bag. If a bulb is picked at random, what is probability of having either a green or a white bulb? Correct Answer 2/3 Given, Green = 3 Orange = 4 White = 5 Total = 12 Either a green and white = 8 ∴ Probability = 812  = 23

Explanation:

Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart , is : Correct Answer 13/102 Given, Total cards = 52 ∴ probability = C112×C113C252 = 13!1!(13 - 1)!×13!1!(13 - 1)!52!2!(52 - 2)! = 13×1352×522 = 13×131326 = 13102

Explanation:

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random . What is the probability of getting a prize ? Correct Answer 2/7 Total element = 10 + 25 = 35 Total event for A lottery = C135 = 35Event of getting A prize  = C110 = 10.'. probability  = 1035 = 27

Explanation:

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ? Correct Answer 9/20 Multiples of 3 or 5 in the range from 1 to 20 : 3,5,6,9,10,12,15 18,20 Total = 9 Probability = 9/20

Explanation:

A bag contains 2 red Roses, 4 yellow Roses and 6 pink Roses. Two roses are drawn at random. What is the probability that they are not of same color? Correct Answer 2/3 Given, Red = 2 Yellow = 4 Pink = 6 Probability  = {1 - (C22C212 + C24C212 + C26C212)} = {1 - (C22 + C24 + C26C212)} = {1 - (2!2!(2 - 2)! + 4!2!94 - 2)! + 6!2!(6 - 2)!12!2!(12 - 2)!)} = {1 - (22×1 + 4×3×22×2 + 6×5×4×3×22×4×3×212×11×10!2×10!)} = {1 - (1 + 6 + 1566)} = 1 - 2266 = 66 - 2266 = 4466 = 23

Explanation:

Once card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack,Queen and King only)? Correct Answer 3/13 1 টি card নেবার মোট ঘটনা C152 12 " face card  হতে 1 টি নেওয়া যাবে C112.'. C152 = 52!1!(52 - 1)! = 52×51!1!×51! = 52and C112 = 12!1!(12 - 1)! = 12×11!1!×11! = 12Probability = C112C152 = 1252 = 313

Explanation:

দুটি ছক্কা একসাথে ফেলে প্রাপ্ত সংখ্যা দুটি যোগ করলে যোগফল ১০ হওয়ার সম্ভবনা কত? সঠিক উত্তর কোনটিই নয় If we roll two dice, there are 6 × 6 = 36 possible outcomes. There are only three different ways of getting a total of 10. 4 + 6 = 10 5 + 5 = 10 6 + 4 = 10 Probability of an event = number of desirable outcomes/total number of possible outcomes P(10) = 3/36 = 1/12

Explanation:

In a class, there are 15 boys and 10 girls . Three students are selected at random. The probability that 1 girl and 2 boys are selected, is - Correct Answer 21/46 Given, Boy's = 15 Girls = 10Total = 25Probability = C215×C110C325 = 105×102300 = 2146 = 21/46

Explanation:

Two dice are thrown simultaneously. What is the probability of getting the sum of the face number is odd? Correct Answer 12 প্রশ্নে বলা হচ্ছে, দুটি ছক্কা নিক্ষেপ করলে যে সংখ্যা দুটি উঠবে তার সমষ্টি বিজোড় হবার সম্ভাবনা কত? এখানে, দুটি ছক্কা নিক্ষেপের পর যে সংখ্যা দুটি উঠবে আর সমষ্টি বিজোড় হবে এরূপ ঘটনাগুলি হলোঃ (1, 2), (1,4), (1, 6), (2, 1)..... এভাবে অনুকূল ঘটনা হবে 1৪টি। আর, দুটি ছক্কা নিক্ষেপের মোট ঘটনা হলো 36টি। নির্ণেয় সম্ভাবনা = অনুকূল ঘটনার সংখ্যা মোট ঘটনার সংখ্যা  = 1836 = 12

Explanation:

লুডু খেলার দুটি ছক্কা একসাথে ফেলে প্রাপ্ত সংখ্যা ২টি যোগ করলে যোগফল ১০ হবার সম্ভবনা কত? সঠিক উত্তর ১/১২ If we roll two dice, there are 6 × 6 = 36 possible outcomes.There are only three different ways of getting a total of 10.4 + 6 = 105 + 5 = 106 + 4 = 10Probability of an event = number of desirable outcomes/total number of possible outcomesP(10) = 3/36 = 1/12

Explanation:

Poppy flipped a coin three times and got heads each time. What is the probability that she gets heads on the next flip? Correct Answer 1/2 মুদ্রাকে একবার নিক্ষেপে Head উঠার সম্ভবনা = 1/2 অতএব, একটি কয়েনকে 3 বার নিক্ষেপের পর পরের বার অর্থাৎ ৪র্থ বার নিক্ষেপে Head উঠার সম্ভবনা = 1/2