Aptitude Questions: Probability Set 8

Hello Aspirants. Welcome to Online Quantitative Aptitude Section in AffairsCloud.com. Here we are creating question sample in Probability, which is common for all the  competitive exams. We have included Some questions that are repeatedly asked in bank exams !!

1. A box contains tickets numbered from 1 to 24. 3 tickets are to be chosen to give 3 prizes. What is the probability that at least 2 tickets contain a number which is multiple of 3? 
   A) 35/256
   B) 33/220
   C) 63/253
   D) 43/190
   E) 59/253
   
   Answer & Explanation

   C) 63/253
   Explanation:
   From 1 to 24, there are 8 numbers which are multiple of 3
   Case 1: 2 are multiple of 3, and one any other number from (24-8) = 16 tickets
   ⁸C₂*¹⁶C₁ / ²⁴C₃ = 56/253
   Case 2: all are multiples of 3.
   ⁸C₃ / ²⁴C₃ = 7/253
   Add both cases.
   
   
   
2. A box contains 6 blue, 5 green and 4 red balls. Two balls are drawn at random. What is the probability that there is no red ball?
   A) 3/30
   B) 11/21
   C) 5/18
   D) 11/23
   E) None of these
   
   Answer & Explanation

   B) 11/21
   Explanation:
   Total balls = 15
   Not red means green or blue i.e. any of (5+6) = 11 balls
   So prob. = ¹¹C₂ / ¹⁵C₂
   
   
   
3. From a pack of 52 cards, 2 cards are drawn at random. What is the probability that both cards are black card or  heart card?
   A) 31/102
   B) 21/73
   C) 1/5
   D) 17/100
   E) 3/10
   
   Answer & Explanation

   A) 31/102
   Explanation:
   Prob. of black card:
   ²⁶C₂ / ⁵²C₂ = 25/102
   Prob. of heart card:
   ¹³C₂ / ⁵²C₂ = 3/51
   Add both cases.
   
   
   
4. Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are jacks?
   A) 62/221
   B) 21/312
   C) 5/21
   D) 55/221
   E) None of these
   
   Answer & Explanation

   D) 55/221
   Explanation:
   There are total 26 cards black, and 4 jacks in which 2 are black jacks
   So case 1: both are black
   ²⁶C₂/⁵²C₂
   case 2: both are jack
   ⁴C₂/⁵²C₂
   Add both cases.
   But now 2 black jacks have been added in both cases, so subtracting their prob. : ²C₂/⁵²C₂
   So 325/1326 + 6/1326 – 1/1326
   
   
   
5. From a group of 3 men, 4 women and 2 children, 4 people are to be chosen to form a committee. What is the probability that the committee contains 1 each of men, women and children?
   A) 4/15
   B) 12/21
   C) 4/19
   D) 11/31
   E) None of these
   
   Answer & Explanation

   B) 12/21
   Explanation:
   Case 1: Prob. when 2 men, 1 woman and 1 child
   ³C₂*⁴C₁*²C₁ /⁹C₄ = 4/21
   Case 2: Prob. when 1 man, 2 women and 1 child
   ³C₁*⁴C₂*²C₁ /⁹C₄ = 2/7
   Case 3: Prob. when 1 man, 1 woman and 2 children
   ³C₁*⁴C₁*²C₂ /⁹C₄ = 2/21
   
   
   
6. A box contains 25 bulbs out of which 5 are defective. 3 bulbs are to be delivered to a customer. What is the probability that he get one defective bulb?
   A) 19/46
   B) 25/51
   C) 44/77
   D) 21/46
   E) None of these
   
   Answer & Explanation

   A) 19/46
   Explanation:
   ⁵C₁*²⁰C_2^/25C3
   
   
   
7. There are 4 red balls, 5 white and 3 green balls in a basket. 3 balls are chosen at random. What is the probability that there is at most 1 green ball?
   A) 13/40
   B) 48/55
   C) 25/68
   D) 8/33
   E) 9/19
   
   Answer & Explanation

   B) 48/55
   Explanation:
   Case 1: 0 green ball means all three red or white balls
   ⁹C₃/¹²C₃
   Case 2: 1 green ball and two red or white balls
   ⁹C₂*³C₁/¹²C₃
   Add both cases.
   
   
   
8. A bag contains 3 red, 4 green and 3 yellow balls. If 2 balls are drawn at random, what is the probability that they are of different color?
   A) 9/16
   B) 4/15
   C) 11/15
   D) 5/11
   E) None of these
   
   Answer & Explanation

   C) 11/15
   Explanation:
   This will be = 1- prob.(both are same in color)
   Prob. of both same in color = [³C₂+⁴C₂+³C₂]/¹⁰C₂ = 12/45
   So required prob. = 1 – 12/45
   
   
   
9. There are 4 black balls and 6 white balls. 2 balls are drawn one by one without replacement. What is the probability that the balls are same in color?
   A) 9/21
   B) 8/17
   C) 5/14
   D) 7/15
   E) 9/19
   
   Answer & Explanation

   D) 7/15
   Explanation:
   When both black, prob. = 4/10 * 3/9
   When both white, prob. = 6/10 * 5/9
   Add both cases.
   
   
   
10. A bag contains 5 red balls and 4 green balls. What is the probability that both balls are same in color?
    A) 5/11
    B) 4/9
    C) 3/13
    D) 6/17
    E) None of these
    
    Answer & Explanation

    B) 4/9
    Explanation:
    Case 1: both red
    ⁵C₂/⁹C₂
    Case 2: both green
    ⁴C₂/⁹C₂
    Add both cases