Question

Coin 1 and Coin 2 are biased coins. The probability that tossing Coin 1 results in head is 0.3. The probability that tossing Coin 2 results in head is 0.9. Coin 1 and Coin 2 are tossed

(i) What is the probability that the result of Coin 1 is tail and the result of Coin 2 is head?

(ii) What is the probability that at least one of the results is head?

(iii) What is the probability that exactly one head appears?

(iv) What is the probability that the result of Coin 1 is head given that head appears exactly once?

Answer 1

i)

probability that the result of Coin 1 is tail and the result of Coin 2 is head=(1-0.3)*0.9=0.63

ii)

probability that at least one of the results is head =1-P(both are tails)=1-(1-0.3)*(1-0.9)=0.93

iii)

probability that exactly one head appears =P(coin 1 head and coin 2 tails)+P(coin 1 tail and coin 2 heads)

=0.3*(1-0.9)+(1-0.3)*0.9=0.66

iii) probability that the result of Coin 1 is head given that head appears exactly once

=P(coin 1 head and 2 tails)/P(exactly 1 head)=0.3*(1-0.9)/0.66=0.0455