Question

suppose that you are offered the following \deal.\ you roll a six sided die. if you roll a 2, 3, 4 or 5, you win $5. otherwise, you pay $10.
a. complete the pdf table. list the x values, where x is the profit, from smallest decimal places where appropriate.
probability distribution table

x	p(x)
-10	0.1667
-5	0.6667
-3	0.1667

b. find the expected profit. $-7.17 (round to the nearest cent)

Explanation:

Step1: Determine the correct $X$ values

The profit $X$ is $- 10$ when rolling a 1 or 6 (2 out of 6 cases), and $X = 5$ when rolling a 2, 3, 4 or 5 (4 out of 6 cases).

Step2: Calculate probabilities

The probability of rolling a 1 or 6 is $P(X=-10)=\frac{2}{6}\approx0.3333$. The probability of rolling a 2, 3, 4 or 5 is $P(X = 5)=\frac{4}{6}\approx0.6667$.

Step3: Calculate the expected value formula

The expected - value formula is $E(X)=\sum_{i}x_{i}P(x_{i})$. Here, $E(X)=(-10)\times0.3333 + 5\times0.6667$.

Step4: Perform the calculation

$E(X)=- 3.333+3.3335=0$.

Answer:

a.

$X$	$P(X)$
5	0.6667

b. $0$