en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

What is the probability of getting either a club or a jack when drawing a single card from a deck of 52 cards?

Solution

What is the probability of getting either a club or a jack when drawing a single card from a deck of 52 cards?

Solution

\frac{4}{13}

Solution steps

Find the probability of getting either a club:

\frac{1}{4}

Find the probability of a jack when drawing a single card from a deck of 52 cards:

\frac{1}{13}

Find the probability of getting either a club and a jack when drawing a single card from a deck of 52 cards:

\frac{1}{52}

Use the Inclusion-Exclusion formula

P (X \lor Y) = P (X) + P (Y) - P (X \land Y)

= \frac{1}{4} + \frac{1}{13} - \frac{1}{52}

\frac{1}{4} + \frac{1}{13} - \frac{1}{52} = \frac{4}{13}

= \frac{4}{13}

Popular Examples

Darnel and Isabelle deposit 8,000.00 into a savings account which earns 15% interest compounded quarterly. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend?Six times a number decreased by 19 equals 2 times a number plus 17.the sum of 8 times a number and 7 is 5 The sum of an integer and 5 times the next consecutive integer is 29. Find the value of the lesser integer.You invest 800 into your account. The account earns 1.5%, compounded weekly. How much money would be in your account after 10 years?