Question

Four cards are drawn at random from a standard deck of 52 cards.

a. What’s the probability that at least one card is a 7?

b. What’s the probability that 3 of the 4 cards are the same suit?

c. What’s the probability that they are all the same suit?

Answer 1

a) Probability that at least one of the card out of the 4 cards drawn is a 7 is computed here as:

= 1 - Probability that there is no 7 in the 4 cards drawn

= 1 - (Number of ways to select 4 cards from the 48 non seven cards / Total ways to select 4 cards from 52 cards)

Therefore 0.2813 is the required probability here.

b) The probability that 3 of the 4 cards are the same suit is computed here as:

= Number of ways to select one of the 4 suits which will have 3 cards of * Number of ways to select 3 cards from that suit * Number of ways to select fourth card from remaining 39 cards / Total ways to select 4 cards from 52 cards

Therefore 0.1648 is the required probability here.

c) The probability that they are all the same suit is computed here as:

= Number of ways to select one of the four suits * Number of ways to select 4 cards from that suit/ Total ways to select 4 cards from 52 cards

Therefore 0.0106 is the required probability here.