en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

You are dealt one card from a 52 card deck. Find the probability that you are dealt a club or a non dash picture card.

Solution

You are dealt one card from a 52 card deck. Find the probability that you are dealt a club or a non dash picture card.

Solution

\frac{10}{13}

Solution steps

Find the probability of you are dealt a club:

\frac{1}{4}

Find the probability of a non dash picture card:

\frac{9}{13}

Find the probability of you are dealt a club and a non dash picture card:

\frac{9}{52}

Use the Inclusion-Exclusion formula

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

= \frac{1}{4} + \frac{9}{13} - \frac{9}{52}

\frac{1}{4} + \frac{9}{13} - \frac{9}{52} = \frac{10}{13}

= \frac{10}{13}

Popular Examples

Meg invested 16,000 in a savings account. If the annual interest rate is 6%, how much will be in the account in5 years with quarterly compounding?Jeanette is saving up money to buy a car. Jeanette puts 5,444.00 into an account which earns 10% interest, compounded quarterly. How much will she have in the account after 3 years?You are dealt one card from a 52-card deck. Find the probability that you are dealt a nine or a red card.Five times the sum of a number and 7 is 30. Find the numbers How much would you need to deposit in an account now in order to have 4000 in the account in 15 years? Assume the account earns 4% interest compounded monthly.