Quantitative Aptitude: Probability Questions – Set 8

  1. A basket contains 8 Blue and 10 Brown balls. There is another basket which contains 6 Blue and 8 Brown balls. One ball is to drawn from either of the two baskets. What is the probability of drawing a Blue ball?
    55/126
    55/63
    37/126
    46/63
    None
    Option A
    Solution:
    P(choosing 1 basket)=1/2
    P(Blue ball from 1st basket)=1/2*8C1/18C1=4/18
    P(Blue ball from 2nd basket)=1/2*6C1/14C1=3/14
    P=4/18+3/14=55/126.
  2. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either a black card or a queen?
    7/9
    4/9
    11/13
    7/13
    None
    Option D
    Solution:
    There are 26 black cards and 4 queen(2queen included in black cards)
    P=(26C1+2C1)/52C1
    28/52=7/13.
  3. A bag contains 12 Green and 8 White balls. Four balls are drawn out one by one and not replaced. What is the probability that they are in alternate colours?
    310/2425
    308/4845
    284/2425
    273/4845
    None
    Option B
    Solution:
    P=12C1/20C1* 8C1/19C1*11C1/18C1*7C1/17C1
    =12/20*8/19*11/18*7/17
    =308/4845.
  4. From a group of 4 men, 5 women and 3 children, 4 people are to be chosen to form a committee. What is the probability that the committee contains at least 1 each of men, women and children?
    16/21
    6/11
    10/11
    7/11
    None
    Option B
    Solution:
    No of ways 2M+1W+1C or 1M+2W+1C or 1M+1W+2C
    P=(4C2*5C1*3C1 + 4C1*5C2*3C1+ 4C1*5C1*3C2)/12C4
    =(90+120+60)/495
    =270/495=6/11.
  5. 8 persons are seated at a round table. What is the probability that 3 particular persons sit together?
    2/9
    4/9
    1/7
    2/7
    None
    Option C
    Solution:
    3 particular person always sit together, then total person =5+1=6
    6 persons will sit in (6-1)!=5! At round table.
    No of ways in which 3 persons always sit together=5!*3!
    No of ways of sitting 8 persons at round table=(8-1)!=7!.
    Then P= (5!*3!)/7! =1/7.
  6. In a lottery, there are 12prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
    12/37
    1/9
    15/37
    2/7
    None
    Option A
    Solution:
    P=12C1/37C1
    =12/37.

Question 7-8: In a bag , there are 5 Blue, 7 white and some Red balls. A ball is randomly selected and the probability that the ball is red is 2/5.

  1. ind the total number of balls?
    22
    24
    18
    20
    None
    Option D
    Solution:
    Total probability=1
    P(Red)=2/5
    Then P(Blue and White)=1-2/5=3/5
    3/5………. 12(5+7)
    1 ……… ?==> 20balls.
  2. If two balls are selected randomly, then what is the probability the selected balls are of same colour?
    47/190
    59/190
    13/80
    17/80
    None
    Option B
    Solution:
    P(balls are of same colour)=(5C2+7C2+8C2)/20C2
    =(10+21+28)/190
    =59/190.
  3. A and B wrote an exam. The probability of A’s pass is 2/7 and the probability of B’s pass is 2/5. What is the probability that only one of them is passed out?
    17/35
    4/7
    18/35
    3/7
    None
    Option C
    Solution:
    A’= A’s fail and B’= B’s fail.
    Therefore, p(A) = 2/7 and p(B) = 2/5,
    P(A’) = 1 – P(A) = 1- 2/7 = 5/7 and P(B’) = 1- P(B) = 1- 1/5 = 4/5
    Required probability= (2/7 * 4/5) + (2/5 * 5/7)
    = (8/35 + 10/35) = 18/35.
  4. In a school, 35% of the students play chess,45% play carom and 10% play both. If a student is selected at random, then the probability that he plays chess or carom is
    1/10
    2/5
    7/10
    3/10
    None
    Option C
    Solution:
    P(A or B)=P(A) + P(B)-P(A and B)
    =35/100+45/100-10/100
    =70/100=7/10.



 

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5 Thoughts to “Quantitative Aptitude: Probability Questions – Set 8”

    1. AmRITa @ bank po

      Hiii from odisha??

  1. AmRITa @ bank po

    No9-p(b)=2/5(not 1/5)
    No3-again starting from white

  2. the walking dead

    🙂

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