Quants Questions: Probability Set 5

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  1. The probability of two persons of passing the interview are 1/3 and 3/5. Then calculate the probability that only one of them pass the interview ?
    a) 7/15
    b) 8/15
    c) 11/15
    d) 13/15
    Answer & Solution
    Answer – b) 8/15
    Solution :
    PF + FP (P = pass, F = fail)
    1/3*2/5 + 2/3*3/5 = 8/15
  2. Among a group of 5 boys and 6 girls, 4 members is to be selected for an event. Find the probability that at least one boy is selected ?
    a) 17/22
    b) 19/22
    c) 21/22
    d) 15/22
    Answer & Solution
    Answer – c) 21/22
    Solution :
    sol = 1 – no boy is selected
    1 – 6c4/11c4 = 21/22
  3. The probability that the problem will be solved by three persons are 1/2, 1/3 and 1/6. Find the probability that the problem is solved ?
    a) 11/18
    b) 13/18
    c) 15/18
    d) 17/18
    Answer & Solution
    Answer – b) 13/18
    Solution :
    1 – 1/2*2/3*5/6 = 13/18
  4. A urn contains 4 red balls, 5 green balls and 6 white balls, If one ball is drawn at random, find the probability that it is neither red nor white ?
    a) 1/3
    b) 1/4
    c) 1/5
    d) 2/3
    Answer & Solution
    Answer – a) 1/3
    Solution :
    5c1/15c1 = 1/3
  5. An elevator starts with 4 passenger and stops at 7 floors of an apartment. Find the probability that all 4 passengers travel to different floor ?
    a) 110/343
    b) 120/343
    c) 18/49
    d) 139/343
    Answer & Solution
    Answer  – b) 120/343
    Solution :
    Total number of outcomes = 7*7*7*7
    Favourable outcome = 7*6*5*4
    P = (7*6*5*4)/7*7*7*7 = 120/343
  6. A five digit number is formed from the numbers 1,3,5,7,8 and 9 without repeating the numbers. Find the probability that the number is divisible by 5 ?
    a) 1/4
    b) 1/5
    c) 1/6
    d) 1/7
    Answer & Solution
    Answer – c) 1/6
    Solution :
    Total number of outcome = 6*5*4*3*2
    Favourable outcome = 5*4*3*2. So, P = 1/6
  7. From a deck of 52 cards, a card is selected and without replacing the card a new card is selected. Find out the probability that the first card is an ace and second card is a king ?
    a) 4/52*3/51
    b) 4/51*3/52
    c) 4/52*4/51
    d) 3/52*3/51
    Answer & Solution
    Answer-c) 4/52*4/51
    Solution :4/52*4/51
  8. The probability that a person will be alive after 20 years is 1/4 and that of his wife is 2/5. Find out the probability that both are not alive after 20 years ?
    a) 7/20
    b) 9/20
    c) 11/20
    d) 13/20
    Answer & Solution
    Answer – b) 9/20
    Solution :
    prob. That man is not alive = 3/4 and that of his wife = 3/5
    Prob. That both will be dead = 3/4*3/5 = 9/20
  9. (Q 9 -10) Three coins are tossed simultaneously.
    Find out the probability that there is at least 2 heads ?
    a) 1/2
    b) 1/4
    c) 1/6
    d) 1/8
    Answer& Solution
    Answer- a) 1/2
    Solution :
    Sol = Total outcomes = {HHH,HTH,HHT,THH,TTT,TTH,THT,HTT}
    Favourable outcome = HHH, HTH, HHT,THH
    Prob = 4/8 = 1/2
  10. Find the probability that there is exactly two tails ?
    a) 3/8
    b) 5/8
    c)7/8
    d) 1/8
    Answer & Solution
    Answer  – a) 3/8
    Solution :
    Favourable outcome = TTH, THT, HTT
    So, prob. = 3/8

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