Question

In a state's Pick 3 lottery game, you pay $1.42 to select a sequence of three digits (from 0 to 9), such as 966. If you select the same sequence of three digits that are
drawn, you win and collect $264 25. Complete parts (a) through (e)

Answer 1

The lottery game is an illustration of probability

• The total number of different selections is 1000
• The probability of winning is 0.001
• The net profit of winning is $262.82
• The expected earning is -$1.156

The number of selections

Each of the three selections can be any of the 1o digits 0 - 9.

So, the total number of different selections is:

$n = 10^3$

$n = 1000$

The probability of winning

Only one of the 1000 selections can win.

So, the probability of winning is:

$p = \frac 1{1000}$

$p = 0.001$

The net profit

The stake amount is given as $1.42, and the earnings per game is given as $264.25.

So, the net profit is:

Net = $264.25 - $1.42

Net = $262.82

The expected winnings

This is calculated as:

$E(x) = \sum x P(x)$

So, we have:

$E(x) = 262.82 * 0.001 - 1.42 * (1 - 0.001)$

$E(x) = -1.156$

Hence, the expected earning is -$1.156

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