Question

Suppose you pay $ 3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 4 or a 1, nothing otherwise. Build the probability distribution for this game. What is the expected amount you win

Answer 1

To build the probability distribution for this game, we determine the probabilities of each possible outcome and their associated amounts won/lost. The expected amount is found by multiplying each amount by its probability and summing them up.

Step-by-step explanation:

To build the probability distribution for this game, we need to determine the probabilities of each possible outcome. In this case, there are two outcomes that result in winning $5.00: rolling a 4 or a 1. There are four other outcomes that result in losing $3.00: rolling a 2, 3, 5, or 6. The probability of rolling a 4 or a 1 is 2/6, since there are two favorable outcomes out of six possible outcomes. The probability of losing is 4/6. We can now build the probability distribution:

Outcome P(X)Amount won/lost4 or 12/6$5.002, 3, 5, or 64/6-$3.00

To find the expected amount you win, we multiply each amount by its corresponding probability and sum them up. The expected amount is (2/6 * $5.00) + (4/6 * -$3.00). Simplifying this expression gives us an expected amount of -$1.00.

Answer 2

- 4/3

Step-by-step explanation:

Given that:

Amount paid to bet = $3

Net winning if 4 or 1 is rolled = $(5 - 3) = $2

If otherwise = loss of $3 (amount paid to play)

Probability of getting a winning :

P( 1 or 4) :

Probability = required outcome / Total possible outcomes

Winning:

Sample space = (1, 2, 3, 4, 5, 6)

P(1 or 4) = 1/6 + 1/6 = 2/6 = 1/3

Losing:

1 - P(winning) = 1 - 1/3 = 2/3

Hence,

The expected Probability :

X = 2, - 3

P(x) = 1/3, 2/3

Σ(x * p(x)) = 2(1/3) + (-3)(2/3)

= 2/3 - 6/3

= 2/3 - 2

= - 4/3