Suppose a coin has probability p of landing on heads. What is the probability of obtaining heads an even number of times in n tosses of the coin? Let yn be the probability of obtaining heads an even number of times in n tosses. Then y0 = 1 since, if you make no tosses, you get zero heads, and zero is an even number. The tree diagram in Fig. 4 displays the probabilities associated with n tosses for n ( 1.

Figure 4 Tree diagram for probability problem with H = heads, T = tails
(a) Use the tree diagram to obtain a difference equation for yn.
(b) Solve the difference equation in part (a)?

Transcribed Image Text:

First Remaining n - 1 Tosses Toss Odd number Yn- of heads н 1- Yn-1 Even number of heads Yn-1 Even number of heads 1-PT. Odd number 1- Yn-1 of heads