Answer:
The expected value for purchasing one ticket for the jackpot = $77.26
Explanation:
We first compute the probability mass function for the problem.
Probability of winning the jackpot
One has to get all 5 white ball and the one red ball correctly. There are 69 white balls and 26 red balls.
5 white balls can be selected from 69 with order not important, and 1 red ball selected from 26 red balls in
⁶⁹C₅ × ²⁶C₁ ways = 292,201,338 ways
And there are (5! × 1) different combinations of those winning numbers = 120 combinations (since order isn't important for the 5 numbers of the white balls)
Required Probability of winning
= (120 ÷ 292,201,338) = 0.0000004107
= (4.107 × 10⁻⁷)
To win, one would buy a $2 ticket, and win $193 million.
Amount of winnings = 193,000,000 - 2 = $192,999,998
Probability of losing = 1 - (Probability of winning) = 1 - (4.107 × 10⁻⁷) = 1
To lose, one would buy a $2 ticket and win nothing.
Amount of winnings = 0 - 2 = -$2
So, the probability mass function
X | 192,999,998 | -2
p | (4.107 × 10⁻⁷) | 1
Expected value = E(X) = Σ xᵢpᵢ
E(X) = [(192,999,998) × (4.107 × 10⁻⁷)] + (-2)(1)
E(X) = 79.26 - 2 = $77.26
Hope this Helps!!!