Question

Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you place the card back in the deck, shuffle the deck, and draw another card. You repeat this process until you have drawn 20 cards in all. What is the probability of drawing at least 8 spades?

Answer 1

To find the probability of drawing at least 8 spades, we can calculate the probability of drawing exactly 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20 spades, and then add them up.

Let's calculate the probability of drawing exactly 8 spades:
P(8 spades) = C(20, 8) * (1/4)^8 * (3/4)^(20-8)

Similarly, we can calculate the probabilities for drawing 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20 spades.

Finally, we add up all these probabilities to find the probability of drawing at least 8 spades.!