Question

1. drawing a card if a card is drawn from a deck, find the probability of getting these results:

a. a 6 and a spade
b. a black king
c. a red card and a 7
d. a diamond or a heart
e. a black card

Explanation:

Step1: Determine total number of cards

A standard deck has \(n = 52\) cards.

Step2: Calculate probability for part a

There is \(1\) card that is a \(6\) of spades. Probability \(P=\frac{1}{52}\).

Step3: Calculate probability for part b

There are \(2\) black kings (king of spades and king of clubs). Probability \(P = \frac{2}{52}=\frac{1}{26}\).

Step4: Calculate probability for part c

There are \(2\) red \(7\)s ( \(7\) of hearts and \(7\) of diamonds). Probability \(P=\frac{2}{52}=\frac{1}{26}\).

Step5: Calculate probability for part d

There are \(13\) diamonds and \(13\) hearts. But we double - count the intersection (which is \(0\) here). So \(n = 13 + 13=26\). Probability \(P=\frac{26}{52}=\frac{1}{2}\).

Step6: Calculate probability for part e

There are \(26\) black cards. Probability \(P=\frac{26}{52}=\frac{1}{2}\).

Answer:

a. \(\frac{1}{52}\)
b. \(\frac{1}{26}\)
c. \(\frac{1}{26}\)
d. \(\frac{1}{2}\)
e. \(\frac{1}{2}\)