Consider two independent tosses of a fair coin. let a be the event that the first toss results in heads, let b be the event that the second toss results in heads, and let c be the event that in both tosses the coin lands on the same side. show that the events a, b, and c are pairwise independent—that is, a and b are independent, a and c are independent, and b and c are independent—but not independent.

Answer with Step-by-step explanation:

We are given that two independent tosses of a fair coin.

Sample space={HH,HT,TH,TT}

We have to find that A, B and C are pairwise independent.

According to question

A={HH,HT}

B={HH,TH}

C={TT,HH}

{HH}

={HH}

={HH}

P(E)=

Using the formula

Then, we get

Total number of cases=4

Number of favorable cases to event A=2

Number of favorable cases to event B=2

Number of favorable cases to event C=2

If the two events A and B are independent then

Therefore, A and B are independent

Therefore, B and C are independent

Therefore, A and C are independent.

Hence, A, B and C are pairwise independent.

jwjwkwkwkkkdjebd b jdjejdndj he jenej