suppose that you are offered the following \deal.\ you roll a six sided die. if you roll a 2, 3, 4 or 5, you…
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.\na. complete the pdf table. list the x values, where x is the profit, from smallest decimal places where appropriate.\nprobability distribution table\n|x|p(x)|\n|-10|0.1667|\n|-5|0.6667|\n|-3|0.1667|\nb. find the expected profit. $-7.17 (round to the nearest cent)
Answer
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.
| $X$ | $P(X)$ |
|---|---|
| -10 | 0.3333 |
| 5 | 0.6667 |
| b. $0$ |