A coin is tossed three times. Let the events A B, and C be defined as follows; A= first toss is head, B= second toss is head, and C= exactly two heads are tossed in a row. Check the independence of i. A and B ii. B and C and iii. C and A

Explanation

Sample space `(S)={(HHH),(HHT),(HTH),(HT T ),(THH),(THT),(T TH),(T T T)}`


Given: (A)= first toss is head


`(A)={(HHH), (HTH), (HHT), (HT T )}`


Given: (B )= second toss is head


`(B )={(HHH), (HHT), (THT), (THH)}`


`P(A)=frac{4}{8}=frac{1}{2}`


`P(B)=frac{4}{8}=frac{1}{2}`


`A cap B={(H H H), (H H T)}`


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