Problem

One card is drawn from an ordinary deck of 52 cards. Find the probabilities of drawing the following cards.
a. $\mathrm{A} 9$ or a 6
b. A 2 or a spade
a. What is the probability that the card is either 9 or a 6 ?
(Simplify your answer. Leave your answer as a fraction.)
b. What is the probability that the card is either a 2 or a spade? $\square$
(Simplify your answer. Leave your answer as a fraction.)

Answer

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Answer

\( \boxed{\frac{4}{13}} \) is the final answer for part b.

Steps

Step 1 :Calculate the probability of drawing a 9 or a 6 from a deck of 52 cards. There are 4 nines and 4 sixes in the deck.

Step 2 :Add the probabilities of drawing a 9 and a 6 together: \( \frac{4}{52} + \frac{4}{52} \)

Step 3 :Simplify the probability: \( \frac{8}{52} \) or \( \frac{2}{13} \)

Step 4 :\( \boxed{\frac{2}{13}} \) is the final answer for part a.

Step 5 :Calculate the probability of drawing a 2 or a spade from a deck of 52 cards. There are 4 twos and 13 spades in the deck.

Step 6 :Subtract the overlap of the 2 of spades to avoid double-counting: \( \frac{4}{52} + \frac{13}{52} - \frac{1}{52} \)

Step 7 :Simplify the probability: \( \frac{16}{52} \) or \( \frac{4}{13} \)

Step 8 :\( \boxed{\frac{4}{13}} \) is the final answer for part b.

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