Suppose that 5 coins are tossed. What would be the probability of having 3 heads?
• All kings, jacks, diamonds have been removed from a pack of 52 playing cards and the remaining cards are well shuffled. A card is drawn from the remaining pack. Find the probability that the card drawn is:
a. a red queen
b. a face card
c. a black card
d. a heart
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Explanation:
The probability of having 3 heads when 5 coins are tossed can be calculated using the binomial distribution. The formula for the probability of getting k successes in n independent Bernoulli trials with probability p of success in each trial is:
P(k) = (n choose k) * p^k * (1-p)^(n-k)
In this case, n=5, k=3, and p=0.5 (assuming a fair coin), so the probability of getting 3 heads is:
P(3 heads) = (5 choose 3) * 0.5^3 * 0.5^2 = 0.3125
Therefore, the probability of getting 3 heads when 5 coins are tossed is 0.3125 or 31.25%.
For the second question,
a. There are two red queens in the deck, so the probability of drawing a red queen is 2/36 or 1/18.
b. There are 12 face cards (4 jacks, 4 queens, and 4 kings) in the deck, so the probability of drawing a face card is 12/36 or 1/3.
c. There are 26 black cards (13 clubs and 13 spades) out of 36 remaining cards, so the probability of drawing a black card is 26/36 or 13/18.
d. There are 9 hearts left in the deck out of 36 remaining cards, so the probability of drawing a heart is 9/36 or 1/4.