Agnes has a weighted coin so that heads comes up 23 of the t

Agnes has a weighted coin so that heads comes up 2/3 of the time. She tosses her coin five

times. What is the probability that heads will appear for the first time on toss 5?

Solution

Probabilty of Heads, P(H) = 2/3

Probabilty of Tails, P(T) = 1 - P(H) = 1/3

Probability of getting Heads for the first time on toss 5 = P ( Tails on first 4 toss and H on fifth toss )                  = P(T) x P(T) x P(T) x P(T) x P(H) = 1/3 x 1/3 x 1/3 x 1/3 x 2/3 = 2/243