Someone rolls a die and then picks cards from a standard 52 card deck equal to the number showing on the die.
a) What is the probability that the number of jacks in the hand equals 2?
b) Conditional on knowing the number of jacks in the hand equals 2, what is the conditional probability that the die showed 3?
My attempt at the solution:
a) chance of getting 2+ on die = 5/6
chance of getting 2 jacks = 2/52 = 1/26
1/26 * 5/6 = 5/156
b) p(dieshowed3|2jacksinhand) = p(dieshowed3 and 2jacksinhand) / p(2jacksinhand)
= ( 1/6 * 1/26 ) / (1/26)
= 1/6
a) What is the probability that the number of jacks in the hand equals 2?
b) Conditional on knowing the number of jacks in the hand equals 2, what is the conditional probability that the die showed 3?
My attempt at the solution:
a) chance of getting 2+ on die = 5/6
chance of getting 2 jacks = 2/52 = 1/26
1/26 * 5/6 = 5/156
b) p(dieshowed3|2jacksinhand) = p(dieshowed3 and 2jacksinhand) / p(2jacksinhand)
= ( 1/6 * 1/26 ) / (1/26)
= 1/6