Question

a card is selected at random from a standard deck of 52 playing cards. find the probability of each event.
(a) randomly selecting a red suit or a 9
(b) randomly selecting a spade or an ace
(c) randomly selecting a 3 or a face card

(a) the probability of randomly selecting a red suit or a 9 is 0.538.
(type an integer or decimal rounded to three decimal places as needed.)
(b) the probability of randomly selecting a spade or an ace is □.
(type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Use the formula for the probability of the union of two events

The formula is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\).
For part (b), let \(A\) be the event of selecting a spade and \(B\) be the event of selecting an ace.
The number of spades \(n(A) = 13\), the number of aces \(n(B)=4\), and the number of cards that are both spade and ace (i.e., the ace of spades) \(n(A\cap B) = 1\).
The total number of cards \(n = 52\).

Step2: Calculate \(P(A)\), \(P(B)\) and \(P(A\cap B)\)

\(P(A)=\frac{n(A)}{n}=\frac{13}{52}\), \(P(B)=\frac{n(B)}{n}=\frac{4}{52}\), \(P(A\cap B)=\frac{n(A\cap B)}{n}=\frac{1}{52}\).

Step3: Calculate \(P(A\cup B)\)

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Answer:

\(0.308\)