Question: A standard deck of cards contains 52 cards. One card is selected from the deck.
(a)compute the probability of randomly selecting a spade or club
(b)Compute the probability of randomly selecting a spade or club or heart.
(c)compute the probability of randomly selecting a jack or heart.
I can’t seem to know what formula to use for this question.
Answer: To solve this problem, you must use two important concepts about probability:
Identifying the Sample Space/possible outcomes & The Addition Rule.
First, there are 52 cards in the deck, so the total number of outcomes is 52. But there are only 13 spades and 13 clubs, so that is the sample space.
The probability of getting a spade, P(Spade), is 13/52 or 0.2500. Same for the probability of getting a club, P(Club) = 13/52 or 0.2500.
To find out the probability of getting a spade or a club, we must know if the events are mutually exclusive. Because a drawn card cannot be both a spade and a club, the events are mutually exclusive.
That means the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B) can be simplified to
P(A or B) = P(A) + P(B).
Thus, the P(Spade or Club) = P(Spade) + P(Club) or 0.2500+0.2500 = 0.5000.
Similarly, the P(Spade or Club or Heart) = 0.2500 + 0.2500 + 0.2500 = 0.7500.
The last part of the question is P(Jack or Heart). Since a card can be both a Jack and a Heart, the two are not mutually exclusive and we need to use the complete Addition Rule: P(A or B) = P(A) + P(B) – P(A and B).
The P(Jack) is 4/52 or 0.0769. P(Heart) is 13/52 or 0.2500. Since there is only one Jack of Hearts, P(Jack and Heart) is 1/52 or 0.0192.
Substituting these values, we find P(Jack or Heart) = 0.0769 + 0.2500 + 0.0192 = 0.3077
Hope this helps!