Question

A standard deck of cards has 52 cards, 4 of each type (Ace, King, Queen, Jack, 10,...,2). From a well-shuffled deck, you are dealt a hand of 5 cards (without replacement).

(a) What is the probability that you are dealt at least one face card (that is a king, queen or jack)?
(b) What is the probability that you are dealt with both; at least one ace and at least one face card?

Answer 1

a)%85,5

b)%92,2

Explanation:

a) To determine the probability of getting a hand with at least one face, we need to calculate the probability of the hand without any face firstly.

`(36/52)*(35/51)*(34/50)*(33/49)*(32/48)=0,145`

Then, we need to deduct this value from the probability 1

`1-0,145=0,855`

The probability of the hand with at least one face is %85,5.

b)To determine the probability of a hand with at least one ace and face we will track the same road again.

`(32/52)*(31/51)*(30/50)*(29/49)*(28/48)=0,0775`

Then, we need to deduct this value from the probability 1

`1-0,0775=0,922`

The probability of the hand with at least one ace and one face is %92,2.