Math Problem Statement

Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws three hearts in succession from a standard deck of 5252 cards without replacement, you give him $40$⁢40. Otherwise, he pays you $10$⁢10. What is the expected value of your bet? Round your answer to the nearest cent, if necessary. just the answer

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Expected Value
Combinatorics

Formulas

P(A) = number of favorable outcomes / total outcomes
Expected Value = (probability of win * amount won) + (probability of loss * amount lost)

Theorems

Law of Total Expectation

Suitable Grade Level

Grades 9-12