Two cards are drawn from a standard 52 card deck.
a) what is the probability that both cards drawn are black?
b) what is the probability that one card is red and the other is black?
c) what is the probability that a two face cards are drawn?
d)what is the probability that two red face cards are drawn?
To determine the probability of each event, we first need to calculate the total number of possible outcomes and the number of favorable outcomes for each scenario.
a) Probability of drawing two black cards:
Total number of possible outcomes = 52 cards (since it's a standard 52-card deck)
Number of favorable outcomes = 26 black cards
Probability = Number of favorable outcomes / Total number of possible outcomes
= 26 / 52
= 1/2
Therefore, the probability that both cards drawn are black is 1/2 or 0.5.
b) Probability of drawing one red card and one black card:
Total number of possible outcomes = 52 cards
Number of favorable outcomes = Number of ways to choose one red card (26) multiplied by the number of ways to choose one black card (26)
Probability = Number of favorable outcomes / Total number of possible outcomes
= (26 * 26) / 52
= 676 / 52
= 13/52
= 1/4
Therefore, the probability that one card is red and the other is black is 1/4 or 0.25.
c) Probability of drawing two face cards:
Total number of possible outcomes = 52 cards
Number of favorable outcomes = Number of ways to choose two face cards (12 face cards: 3 face cards per suit)
Probability = Number of favorable outcomes / Total number of possible outcomes
= 12 / 52
= 3/13
Therefore, the probability that two face cards are drawn is 3/13 or approximately 0.231.
d) Probability of drawing two red face cards:
Total number of possible outcomes = 52 cards
Number of favorable outcomes = Number of ways to choose two red face cards (6 red face cards: King, Queen, or Jack)
Probability = Number of favorable outcomes / Total number of possible outcomes
= 6 / 52
= 3/26
Therefore, the probability that two red face cards are drawn is 3/26 or approximately 0.115.