Question

A card is drawn at random from a well-shaped deck of playing cards. What is the probability that the drawn card is either a red card or a king of clubs?

Answer 1

The probability of drawing either a red card or the king of clubs from a standard 52-card deck is 27 out of 52, or approximately 0.5192.

Step-by-step explanation:

The question is asking about the probability of drawing a specific type of card from a standard deck of 52 playing cards. There are two separate events to consider: drawing a red card, which could be either a heart or a diamond, and drawing the king of clubs specifically.

Let us denote A as the event of drawing a red card and B as the event of drawing the king of clubs. Since there are 26 red cards in a deck (13 hearts and 13 diamonds) and only 1 king of clubs, the probability of event A is P(A) = 26/52 = 1/2, and the probability of event B is P(B) = 1/52.

Since these two events are not mutually exclusive (they cannot both occur simultaneously when drawing a single card), we have to consider the following formula for the probability of either A or B occurring:

P(A or B) = P(A) + P(B) since A and B are mutually exclusive events.

Therefore, P(A or B) = (26/52) + (1/52) = 27/52.

Thus, the probability of drawing either a red card or the king of clubs is 27 out of 52, or approximately 0.5192.