Question

A promising college basketball talent has to decide whether or not to enter this year's NBA draft. If he enters, he expects that there is a 40% chance that he is a first-round pick and a 60% chance that he is picked in a later round. As a first-round pick, he would secure a $10 million contract; if he is picked in a later round, his contract would only be worth $1,000,000.

What is the expected value of entering the NBA draft?
A) $6,000,000
B) $7,000,000
C) $8,400,000
D) $9,200,000

Answer 1

The expected value of entering the NBA draft is $4,600,000.

Step-by-step explanation:

To find the expected value of entering the NBA draft, we multiply the value of each outcome (first-round pick or later round pick) by its corresponding probability, and then sum these values. In this case, the expected value can be calculated as:

(0.4 * $10,000,000) + (0.6 * $1,000,000) = $4,000,000 + $600,000 = $4,600,000

Therefore, the expected value of entering the NBA draft is $4,600,000. Option D, $9,200,000, is not the correct answer.