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Question

Two coins are tossed simultaneously. Find the probability that either both heads or both tails occur

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Solution

When two coins are tossed, sample space S is given by {HH,HT,TH,TT} and therefore, n(S)=4.

Let A denote the event that both head appear that is {HH} and n(A)=1, therefore, probability of both head appear is:

P(A)=n(A)n(S)=14

Let B denote the event that both tail appear that is {TT} and n(B)=1, therefore, probability of both tail appear is:

P(B)=n(B)n(S)=14

Intersection of A and B is the common elements between A and B which is none, thus, n(AB)=0 and

P(AB)=n(AB)n(S)=04=0

Therefore, the events are mutually exclusive.

The probability of either both head or both tail occur is P(AB) and we know that for mutually exclusive event, P(AB)=P(A)+P(B) that is:

P(AB)=P(A)+P(B)=14+14=24=12

Hence, probability that either both heads or both tails occur is 12.


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