Question

5) In the MegaMillions lottery a player buys a $1 ticket and picks five numbers from the numbers 1 to 70. The lottery has a bin with seventy white balls, each with a number from 1 to 70. The lottery picks five balls from the bin with the white balls. If the five numbers the player picked match the numbers drawn on the five white balls then the player wins $1,000,000 (in most states, but not including California, where the rules are different). In addition, the player picks one Mega number from the numbers 1 to 25. The lottery has a bin with twenty-five gold balls, each with a number from 1 to 25. The lottery picks one gold ball from the bin. If the player matches all five numbers on the white balls, plus the number on the gold ball, the player wins the MegaMillions jackpot (which is a minimum of $40 million). Assume you buy your ticket outside of California. Calculate the exact probability of winning exactly $1,000,000 (no more and no less) in the MegaMillions lottery if you buy one ticket. Include 11 decimal points in your answer. In order to earn the extra credit you must show your work. Hint: Use the Multiplication Law for Independent Events.

Answer 1