A dealer selects a card at random from a standard deck of 52 cards.
a) What is the probability the card is a Queen? 1/13
b) What is the probability the card is a 5 or a 10?
c) What is the probability the card is a heart or an Ace?

i think i have the answer for a) as 1/13 cause there are 4 kingdoms(as i like to say) the heart kingdom, spade kingdom, club kingdom, and the diamond kingdom. each one has 13 cards adding them up equals 52 cards. there are 4 queens total one in each kingdom. so the starting fraction would be 4/52 i divided that by 4 on nominator and denominator and got 1/13 chance she could draw a queen. in the simplest form.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.