Quantitative Aptitude: Probability Set 3

Probability Questions for Bank PO Exams – SBI PO, NIACL, NICL, BoB PO, IBPS PO, and other exams

1. There are 100 tickets in a box numbered 1 to 100. 3 tickets are drawn at one by one. Find the probability that the sum of number on the tickets is odd.
   A) 2/7
   B) 1/2
   C) 1/3
   D) 2/5
   E) 3/7
   
   View Answer

   Option B
   Solution:
   There will be 4 cases
   Case 1: even, even, odd
   Prob. = 1/2 × 1/2 × 1/2
   Case 2: even, odd, even
   Prob. = 1/2 × 1/2 × 1/2
   Case 3: odd, even, even
   Prob. = 1/2 × 1/2 × 1/2
   Case 4: odd, odd, odd
   Prob. = 1/2 × 1/2 × 1/2
   Add all the cases, required prob. = 1/2
2. There are 4 green and 5 red balls in first bag. And 3 green and 5 red balls in second bag. One ball is drawn from each bag. What is the probability that one ball will be green and other red?
   A) 85/216
   B) 34/75
   C) 95/216
   D) 35/72
   E) 13/36
   
   View Answer

   Option D
   Solution:
   Case 1:first green, second red
   Prob. = 4/9 × 5/8 = 20/72
   Case 2:first red, second green
   Prob. = 5/9 × 3/8 = 15/72
   Add the two cases
3. A bag contains 2 red, 4 blue, 2 white and 4 black balls. 4 balls are drawn at random, find the probability that at least one ball is black.
   A) 85/99
   B) 81/93
   C) 83/99
   D) 82/93
   E) 84/99
   
   View Answer

   Option A
   Solution:
   Prob. (At least 1 black) = 1 – Prob. (None black)
   So Prob. (At least 1 black) = 1 – (⁸C₄/¹²C₄) = 1 – 14/99
4. Four persons are chosen at random from a group of 3 men, 3 women and 4 children. What is the probability that exactly 2 of them will be men?
   A) 1/9
   B) 3/10
   C) 4/15
   D) 1/10
   E) 5/12
   
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   Option B
   Solution:
   2 men means other 2 woman and children
   So prob. = ³C₂ × ⁷C₂ /¹⁰C₄ = 3/10
5. Tickets numbered 1 to 120 are in a bag. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
   A) 8/15
   B) 5/16
   C) 7/15
   D) 3/10
   E) 13/21
   
   View Answer

   Option C
   Solution:
   Multiples of 3 up to 120 = 120/3 = 40
   Multiples of 5 up to 120 = 120/5 = 24 (take only whole number before the decimal part)
   Multiple of 15 (3×5) up to 120 = 120/15 = 8
   So total such numbers are = 40 + 24 – 8 = 56
   So required probability = 56/120 = 7/15
6. There are 2 people who are going to take part in race. The probability that the first one will win is 2/7 and that of other winning is 3/5. What is the probability that one of them will win?
   A) 14/35
   B) 21/35
   C) 17/35
   D) 19/35
   E) 16/35
   
   View Answer

   Option D
   Solution:
   Prob. of 1st winning = 2/7, so not winning = 1 – 2/7 = 5/7
   Prob. of 2nd winning = 3/5, so not winning = 1 – 3/5 = 2/5
   So required prob. = 2/7 * 2/5 + 3/5 * 5/7 = 19/35
7. Two cards are drawn at random from a pack of 52 cards. What is the probability that both the cards drawn are face card (Jack, Queen and King)?
   A) 11/221
   B) 14/121
   C) 18/221
   D) 15/121
   E) 14/221
   
   View Answer

   Option A
   Solution:
   There are 52 cards, out of which there are 12 face cards.
   So probability of 2 face cards = ¹²C₂/⁵²C₂ = 11/221
8. A committee of 5 people is to be formed from among 4 girls and 5 boys. What is the probability that the committee will have less number of boys than girls?
   A) 7/12
   B) 7/15
   C) 6/13
   D) 5/14
   E) 7/13
   
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   Option D
   Solution:
   Case 1: 1 boy and 4 girls
   Prob. = ⁵C₁ × ⁴C₄/⁹C₅ = 5/146
   Case 2: 2 boys and 3 girls
   Prob. = ⁵C_2 × ⁴C₃/⁹C₅ = 40/126
   Add the two cases = 45/126 = 5/14
9. A bucket contains 2 red balls, 4 blue balls, and 6 white balls. Two balls are drawn at random. What is the probability that they are not of same color?
   A) 5/11
   B) 14/33
   C) 2/5
   D) 6/11
   E) 2/3
   
   View Answer

   Option E
   Solution:
   Three cases
   Case 1: one red, 1 blue
   Prob = ²C₁ × ⁴C₁ / ¹²C₂ = 4/33
   Case 2: one red, 1 white
   Prob = ²C₁ × ⁶C₁ / ¹²C₂ = 2/11
   Case 3: one white, 1 blue
   Prob = ⁶C₁ × ⁴C₁ / ¹²C₂ = 4/11
   Add all cases
10. A bag contains 5 blue balls, 4 black balls and 3 red balls. Six balls are drawn at random. What is the probability that there are equal numbers of balls of each color?
    A) 11/77
    B) 21/77
    C) 22/79
    D) 13/57
    E) 15/77
    
    View Answer

    Option E
    Solution:
    ⁵C₂× ⁴C₂× ³C₂/ ¹²C₆