Question

The probability that a candidate can pass in an exam is 0.6. What is the probability that he pass before the second trial?​

Answer 1

Answer:

two methods are there to solve this question.

Step-by-step explanation:

first find out what is the probability of failing of both . boy passes with probability 3/5 i.e. he fails with probability 1-(3/5)= 2/5.

similarly for girl the probability of failing will be 1-passing probability i.e. 1-(2/5)=3/5

so prob of failing both is (2/5)*(3/5)=6/25.

so the prob of passing at least one of them is 1-(6/25)=19/25.

the second method

at least one of them passing means if boy passes or if girl passes or if both passes .all these three situations mean at least one has passed.

so first case only boy passes (inherently it shows that the girl has failed) =

prob of girl failing and prob of boy passing= (3/5)*(3/5)= 9/25

second case the situation is reverse. prob of girl passing and prob of boy failing=(2/5)*(2/5)=4/25

third scenario if both passes .

then prob is (3/5)*(2/5)=6/5

so adding all we get (9/25)+(4/25)+(6/25)=19/25

note- here we have multiplied some probabilities and added in the end. the logic is if one passes that means our purpose is fulfilled so we will stop. if there is another way to fulfill our purpose then we will ompute and add to the previous one. that's why boy passes we stop at that point and kept that prob aside . again the girl passes in this case our purpose is solved so we have added the prob.

if our purpose is not solved we keep on calculating and multiplying .like boy fails and girl passes. here fist boy fails doesn't fulfill our purpose but the moment girl passes it fulfills our purpose so we have multiplied the prob of boy failing and girl passing.

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