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Question

A player randomly chooses one of the coin A,B. Coin A has a probability of heads 34 and coin B has a probability of heads 14. He tosses the coin twice. The probability that he obtains heads only once is


A

38

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B

58

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C

78

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D

None of these

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Solution

The correct option is A

38


Explanation for the correct option:

Step 1: Find the probability of the head comes on Coin A:

Find the probability that coin A is chosen and the head comes in it.

P(H)=P(A)·PHA=12·2·34·14=316

Step 2: Find the probability of the head comes on Coin B:

Find the probability that coin B is chosen and the head comes in it.

P(H)=P(B)·PHB=12·2·14·34=316

Step 3: Find the probability that head comes on tossing any coin:

Sum up the probability of getting head on any of the coins to get the required probability.

P(H)=316+316=38

Hence, option (A) is the correct answer.


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