Question

A contestant’s final winnings on a game show are determined by a random selection of a base amount and a possible multiplier. For the base amount, the contestant randomly selects one of four cards, where two cards are marked $1,000, one card is marked $2,000, and one card is marked $5,000. After choosing the card, the contestant randomly selects one of five chips, where three chips are red and two chips are white. If the selected chip is red, the contestant’s final winnings are twice the value of the base amount. If the selected chip is white, the contestant’s final winnings are the value of the base amount. What is the probability that a contestant’s final winnings are exactly $2,000?

Answer 1

Answer:

$\frac{8}{25}$ = 0.32

Step-by-step explanation:

Exactly $2000 final winnings is possible only in one of the following two cases:

1)

The chosen card is marked $1000 and then red chip is selected. Because red chip doubles contestant's $1000 base amount, and makes it $2000.  

• Since two cards of the five cards are marked $1000, the probability of choosing $1000 marked card is $\frac{2}{5}$

• Since three of five chips is red, the probability of choosing red chips is $\frac{3}{5}$

Then the probability of both choosing $1000 marked card and red chip is:

$\frac{2}{5}$ × $\frac{3}{5}$ = $\frac{6}{25}$

2)

The chosen card is marked $2000 and then white chip is selected. Because white chip makes the contestant's final winning remain the same as base amount, which is $2000

• Since one card of the five cards are marked $2000, the probability of choosing $2000 marked card is $\frac{1}{5}$

• Since two of five chips is white, the probability of choosing red chips is $\frac{2}{5}$

Then the probability of both choosing $2000 marked card and white chip is:

$\frac{1}{5}$ × $\frac{2}{5}$ = $\frac{2}{25}$

The probability that a contestant's final winning is the sum of probabilities of these two cases:

$\frac{6}{25}$ × $\frac{2}{25}$ = $\frac{8}{25}$= 0.32