Question

Each trial consists of either tossing a fair coin or rolling a fair die. You startwith tossing the coin.As long as it turns out tails you will keep tossing it. The moment it turns outheads you will stop tossing it and start rolling the die. You continue rolling the die until you get a four or a five, then you start tossing the coin again. You keep applyingthe rules described above to change from tossing the coin to rolling the die and vice versa. What is the probability that on the third trial you will toss a coin

Answer 1

0.41665 = 41.665% probability that on the third trial you will toss a coin

Explanation:

First trial: Toss the coin

The following outcomes end up with a coin being tossed on the third trial.

Tails on the first and second trial(each with 0.5 probability).

Heads on the first trial(0.5 probability) and 4 or 5 on the die on the second trial(6 sided die, so 2/6 = 1/3 = 0.3333 probability).

What is the probability that on the third trial you will toss a coin

`p = 0.5^2 + 0.5*0.3333 = 0.41665`

0.41665 = 41.665% probability that on the third trial you will toss a coin