Question

question 31 (1 point) saved if one card is randomly picked from a standard deck of 52 cards, the probability that the card will be a red suit (heart or diamond), or a face card (jack, queen, or king), or both, is 50.0% (26/52) 61.5% (32/52) 76.9% (40/52) 88.5% (46/52)

Explanation:

Step1: Count relevant cards

Number of red - suit cards (Hearts and Diamonds) is 26. Number of face - cards (Jack, Queen, King) is 12. Number of red - suit face - cards is 6.

Step2: Use the inclusion - exclusion principle

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the set of red - suit cards and \(B\) be the set of face - cards or diamonds. The number of diamonds is 13, and face - cards is 12, with 3 face - cards in diamonds. So \(n(B)=13 + 12-3=22\). The number of red - suit cards \(n(A) = 26\), and \(n(A\cap B)=6 + 3=9\) (6 red - face cards and 3 non - red face - diamonds). The total number of cards \(n = 52\).
\[P=\frac{26+22 - 9}{52}=\frac{32}{52}\approx61.5\%\]

Answer:

61.5% (32/52)