Question

here is a table showing all 52 cards in a standard deck. suppose one card is drawn at random from a standard deck. answer each part. write your answers as fractions. (a) what is the probability that the card drawn is a four? (b) what is the probability that the card drawn is a black card? (c) what is the probability that the card drawn is a four or a black card?

Explanation:

Step1: Determine total number of cards

There are 52 cards in a standard deck.

Step2: Calculate probability of drawing a four

There are 4 fours in a deck. So the probability $P(\text{four})$ is $\frac{4}{52}=\frac{1}{13}$.

Step3: Calculate probability of drawing a black card

There are 26 black cards in a deck. So the probability $P(\text{black})$ is $\frac{26}{52}=\frac{1}{2}$.

Step4: Calculate number of fours or black cards

There are 4 fours and 26 black cards. But 2 fours are black (4 of spades and 4 of clubs), so the number of distinct cards that are either four or black is $4 + 26- 2=28$. So the probability $P(\text{four or black})$ is $\frac{28}{52}=\frac{7}{13}$.

Answer:

(a) $\frac{1}{13}$
(b) $\frac{1}{2}$
(c) $\frac{7}{13}$