Question

A bridge hand is defined as 13 cards selected at random and without replacement from a deck of 52 cards. In a standard deck of cards, there are 13 cards from each suit: hearts, spades, clubs, and diamonds. What is the probability of being dealt a hand that does not contain a heart?; X; X; P; X

a) 39/52
b) 3/4
c) 1/4
d) 1/13

Answer 1

The probability of being dealt a hand that does not contain a heart in a bridge hand is 3/4.

Step-by-step explanation:

To find the probability of being dealt a hand that does not contain a heart in a bridge hand, we need to consider the number of favorable outcomes (hands without a heart) and the number of possible outcomes (all possible hands).

There are 39 cards in the deck that are not hearts (52 - 13), so the number of favorable outcomes is the number of ways to choose 13 cards from the 39 non-heart cards.

The total number of possible outcomes is the number of ways to choose 13 cards from the 52 cards in the deck.

Therefore, the probability is given by:

P(hand does not contain a heart) = favorable outcomes / possible outcomes

P(hand does not contain a heart) = C(39, 13) / C(52, 13)

Calculating this probability gives us 39/52, which simplifies to 3/4.