Latest Elitmus Aptitude Question SOLUTION: probability that guy1 will succesfully hit a shot is 2/3. probabilty of guy2 succesfully hitting a shot is 2/3. if they shoot two shots each, what is the probability that they ha

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(#M40155960) ELITMUS Numerical Ability question probability of shooting same Keep an EYE

probability that guy1 will succesfully hit a shot is 2/3. probabilty of guy2 succesfully hitting a shot is 2/3. if they shoot two shots each, what is the probability that they have equal number of hits?

Asked In Elitmus Mukesh Kumar Singh (8 years ago)

Solved Sarthi Chugh Read Solution (4)

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Sarthi Chugh  (8 years ago) Best Solution

Consider these cases:
for 0 hit each: (1 way)
(1/3*1/3)[guy1]*(1/3*1/3)[guy2]
for 1 hit each: (4 ways)
(2/3*1/3)*(2/3*1/3), (2/3*1/3)*(1/3*2/3), (1/3*2/3)*(2/3*1/3), (1/3*2/3)*(1/3*2/3)
for 2 hits each:(1 way)
(2/3*2/3)*(2/3*2/3)

Add all these cases, you will get answer as 11/27.

Is this solution Helpfull? Yes (37) | No (13)  

tanya  (7 years ago)

why are we adding case 0 and case 1 ? the question asks for only 2 shots ..

Is this solution Helpfull? Yes (8) | No (3)  

PANKAJ BHATT  (7 years ago)

using binomial expansion nCr*(P)^r*(1-P)^(n-r), where r is the no of success and n is the attempts(shots taken).
now as each are having equal hits we need to consider all the possibilities & there can be 3 such cases
1) guy1 hits 2 out of 2 AND(*) guy2 also hits 2 out of 2.......so using the above formula we get 16/81
OR(+)
2) guy1 AND guy2 hit 1 out of 2.......we get 16/81
OR
3) both guy1 and guy2 hit 0 in 2 attempts......we get 1/81


so adding 16/81 + 16/81 + 1/81 = 33/81 = 11/27

Is this solution Helpfull? Yes (7) | No (3)  

shivam  (6 years ago)

In four shots he can hit once,twice,thrice,all hit the probability of hitting the target isp(1hit out of 4)+P(2hit out of 4)+p(3hit out of 4)+p(All hit) it is total probability-probability of not hitting yhr target =>1-(3/4*3/4*3/4*3/4) =>175/256

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