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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