# Question

A prisoner is trapped in a cell containing 3 doors. The first door leads to a tunnel that returns him to his cell after 2 days’ travel. The second leads to a tunnel that returns him to his cell after 4 days’ travel. The third door leads to freedom after 1 day of travel. If it is assumed that the prisoner will always select doors 1, 2, and 3 with respective probabilities .5, .3, and .2, what is the expected number of days until the prisoner reaches freedom?

## Answer to relevant Questions

Consider the following dice game: A pair of dice is rolled. If the sum is 7, then the game ends and you win 0. If the sum is not 7, then you have the option of either stopping the game and receiving an amount equal to that ...Each of m + 2 players pays 1 unit to a kitty in order to play the following game: A fair coin is to be flipped successively n times, where n is an odd number, and the successive outcomes are noted. Before the n flips, each ...Consider a gambler who, at each gamble, either wins or loses her bet with respective probabilities p and 1 − p. A popular gambling system known as the Kelley strategy is to always bet the fraction 2p − 1 of your current ...Two envelopes, each containing a check, are placed in front of you. You are to choose one of the envelopes, open it, and see the amount of the check. At this point, either you can accept that amount or you can exchange it ...Suppose that X1 and X2 are independent random variables having a common mean μ. Suppose also that Var(X1) = σ21 and Var(X2) = σ22. The value of μ is unknown, and it is proposed that μ be estimated by a weighted average ...Post your question

0