Question

You are dealt one card from a 52-card deck. Find the probability that you are dealt a nine OR a red card.

Answer 1

Given

There 52 cards in a deck.

To find:

The probability that the given card is a nine or a red card.

Explnation:

It is given that,

There are 52 cards in a deck.

Then,

The number of nine card in the deck of 52 cards is,

$\begin{gathered} n(Nine\text{ }card)=4 \\ n(N)=4 \end{gathered}$

The number of red cards in the deck of 52 cards is,

$\begin{gathered} n(Red\text{ }cards)=26 \\ n(R)=26 \end{gathered}$

Therefore,

$\begin{gathered} P(nine\text{ }card\text{ }or\text{ }red\text{ }cards)=P(N\cup R) \\ \Rightarrow P(N\cup R)=P(N)+P(R)-P(N\cap R) \\ =\frac{n(N)}{n(S)}+\frac{n(R)}{n(S)}-\frac{n(N\cap R)}{n(S)} \\ =\frac{4}{52}+\frac{26}{52}-\frac{2}{52} \\ =\frac{28}{52} \\ =\frac{7}{13} \end{gathered}$

Hence, the probability is, 7/13.