Q. 7

Three coins are tossed simultaneously. Find the probability that all coins show heads if at least one of the coins shows a head.

Answer :


When three coins are tossed simultaneously, the total number of outcomes = 23 = 8, and the sample space is given by S= {(H,H,H),(H,H,T),(H,T,T),(H,T,H),(T,H,T),(T,T,H),(T,H,H),(T,T,T)}


Let P(A) be the probability of getting 3 heads.


The sample space of A = {(H,H,H)}



Let P(B) be the probability of getting at least head.


Probability of one head = 1 – probability of no heads = 1-1/8 = 7/8



The probability that the throw is either all heads or at least one head i.e.


Now,







Tip – By conditional probability, where is the probability of occurrence of the event A given that B has already occurred.


The probability that all coins show heads if at least one of the coins


showed a head:






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