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Chapter 7: Problem 25

If a card is drawn at random from a standard 52 -card deck, what is the probability that the card drawn is a. A diamond? b. A black card? c. An ace?

Short Answer

Expert verified
The probabilities of drawing a diamond, a black card, and an ace from a standard 52-card deck are as follows: a. \( P(diamond) = \frac{13}{52} \) b. \( P(black) = \frac{26}{52} \) c. \( P(ace) = \frac{4}{52} \)

Step by step solution

01

Count the number of diamonds

In a standard deck, there are 13 diamonds (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king).
02

Calculate the probability of drawing a diamond

To find the probability, divide the number of favorable outcomes (drawing a diamond) by the total number of possible outcomes (52 cards). So the probability is, \( P(diamond) = \frac{13}{52} \). #b. A black card#
03

Count the number of black cards

A standard deck has 26 black cards (13 spades and 13 clubs).
04

Calculate the probability of drawing a black card

To find the probability, divide the number of favorable outcomes (drawing a black card) by the total number of possible outcomes (52 cards). So the probability is, \( P(black) = \frac{26}{52} \). #c. An ace#
05

Count the number of aces

In a standard deck, there are 4 aces (one of each suit).
06

Calculate the probability of drawing an ace

To find the probability, divide the number of favorable outcomes (drawing an ace) by the total number of possible outcomes (52 cards). So the probability is, \( P(ace) = \frac{4}{52} \).

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