You draw nine cards from a standard deck of cards. What is the probability that
a. four or more will be red,
b. exactly two or three will be red,
c. two or fewer will be red, and
d. exactly five will be red?.
.74
Draw nine cards from a deck of 52. What is the probability of drawing 4 red, 2 or more reds, 2 or fewer reds, and exactly 5 reds
To calculate the probabilities, we will need to determine the total number of possible outcomes and the number of favorable outcomes for each event.
a. To find the probability that four or more cards will be red, we need to calculate the probability of getting exactly four red cards, five red cards, six red cards, seven red cards, eight red cards, or nine red cards.
- Calculate the number of ways to choose four red cards from a deck of 26 red cards (there are 13 red hearts and 13 red diamonds).
- This can be calculated as: C(26, 4), where C(n, r) represents the number of combinations of n items taken r at a time.
- Next, calculate the number of ways to choose five red cards, six red cards, seven red cards, eight red cards, or nine red cards.
- Finally, we add up all these possibilities to determine the number of favorable outcomes.
- The total number of possible outcomes for drawing nine cards from a standard deck is C(52, 9).
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes.
b. To find the probability that exactly two or three cards will be red, we need to calculate the number of ways to choose exactly two red cards and exactly three red cards separately. Then, we sum up both cases to find the number of favorable outcomes.
c. To find the probability that two or fewer cards will be red, we need to calculate the number of ways to choose zero, one, or two red cards separately and sum up those cases.
d. To find the probability that exactly five cards will be red, we need to calculate the number of ways to choose five red cards from the deck.
Now, let's calculate the actual probabilities using these steps.