Refer to the game of craps described in Excercise 311 A pla

Refer to the game of craps described in Excercise 3.11 ( A player throws both dice, winning uncondiitonally if he produces a natural [the sum of the numbers showing on thw two dice is 7 or 11] and losing uncoditionally if he throws a craps [a 2,3, or 12])

A player casts the dice a single time.

a.) given the sum of the dice is off, what is the probability that craps is throw?

b.) Given that the player does not throw craps, what is the probability that the player throws a double?

I asked my professor and he told me I would use condiitonal probability but I am just not sure how to and how to recognize that I would use conditional probability. Thank you!

Solution

If a condition is given and we have to find the probabilty of any other condition such that the given condition holds then we use conditional probability.

Here in the part (a) it is given the sum of dice is off then we have to find the probability that a craps is thrown.

P[craps is thrown|sum of dice is off]=P[craps is thrown,sum of dice is off]/P[sum of dice is off]

(b)P[a double is thrown|craps not thrown]=P[a double is thrown,craps not thrown]/P[craps not thrown]