Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws two black cards in succession from a standard deck of 52 cards replacing the first card, you give him $30. Otherwise, he pays you $20. If the same bet was made 20 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary.

I am expected to win $150

Step-by-step explanation:

We need to calculate the probability of drawing 2 black cards with replacement

There are 26 black cards in a deck of cards

The probability of drawing a black card is thus 26/52 = 1/2

So the probability of drawing two black cards in succession with replacement will be 1/2 * 1/2 = 1/4

So the probability of not drawing the two in succession will be 1 - 1/4 = 3/4

so out of twenty trials the number of times the drawing will occur will be 1/4 * 20 = 5 times

The number of times it will not occur will be 20-5 = 15 times

The amount my friend will win will be 5 * 30 = 150

The amount I will win will be 20 * 15 = 300

The amount I expect to win in the deal will be 300-150 = $150

x + 4/7

step-by-step explanation:

use cymath