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

- 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

the answer will be

30 people weigh 160 pounds or more