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 15 cards in all. what is the probability of drawing at least 5 spades?

Answer 1

To find the probability of drawing at least 5 spades from a standard deck, we can calculate the probabilities of drawing 5, 6, 7, 8, 9, 10, 11, 12, and 13 spades. Then, we can sum up these probabilities to find the overall probability. This can be done by considering the probability of drawing a spade on each individual draw and using the formula for probability with replacement.

Step-by-step explanation:

To find the probability of drawing at least 5 spades, we need to consider the possible outcomes. There are 52 cards in a standard deck, and 13 of them are spades. Since we are drawing with replacement, the probability of drawing a spade on each draw is 13/52 = 1/4.

The probability of drawing at least 5 spades can be calculated as follows:

Probability of drawing 5 spades: (1/4)^5 = 1/1024

Probability of drawing 6 spades: (1/4)^6 = 1/4096Probability of drawing 7 spades: (1/4)^7 = 1/16384Probability of drawing 8 spades: (1/4)^8 = 1/65536Probability of drawing 9 spades: (1/4)^9 = 1/262144Probability of drawing 10 spades: (1/4)^10 = 1/1048576Probability of drawing 11 spades: (1/4)^11 = 1/4194304Probability of drawing 12 spades: (1/4)^12 = 1/16777216Probability of drawing 13 spades: (1/4)^13 = 1/67108864

To find the probability of drawing at least 5 spades, we need to sum up the probabilities of these outcomes:

Probability of drawing at least 5 spades = (1/1024) + (1/4096) + (1/16384) + (1/65536) + (1/262144) + (1/1048576) + (1/4194304) + (1/16777216) + (1/67108864)

Answer 2

5:15 because you aren't drawing all of the 52 cards so your proportion would be the probability of drawing at least 5 spade and the 15 cards drawn in all