Question

A single card is drawn from a standard deck. Find the probability of the following event. (Enter your probability as a fraction.)Drawing a red card or a face card

Answer 1

The probability of drawing a red card or a face card is 8/13

Step-by-step explanation

Let A be the event of red card, n(A) = 26

Let B represent the event of face card, n(B) = 12

The total possible outcome, n(S) = 52

From mutually exclusive event, (Addition law of probability), we have

p(A∪B) = p(A) + n(B) - p(A∩B)

p(A) = n(A)/n(S) = 26/52

p(B) = n(B)/n(S) = 12/52

But p(A∩B) = 3 + 3 = 6/52 that is (3 clover face cards + 3 spade face cards)

Therefore, the probability of drawing a red card or a face card is

`\begin{gathered} p\mleft(A\cup B\mright)=(26)/(52)+(12)/(52)-(6)/(52) \\ p(A\cup B)=(32)/(52) \\ p(A\cup B)=(8)/(13) \end{gathered}`