Question 4: Please help, I have no idea what the answer is.

Lucy offers to play the following game with Charlie: "Let us show dimes to each other, each choosing either heads or tails. If w

Darya [45]

Answer:

(a)Charlie is right

(b)$0

Step-by-step explanation:

(a)A game is said to be a fair game when the probability of winning is equal to the probability of losing. Mathematically, a game is said to be fair when the expected value is zero.

In the game, the possible outcomes are: HH, HT, TH and TT.

Charlie wins when the outcome is HH, TT

P(Charlie Wins)=2/4
P(Charlie Losses)=2/4

Lucy wins when the outcome is HT or TH

P(Lucy Wins)=2/4
P(Lucy Losses)=2/4

Therefore, the game is fair. Charlie is right.

(b)

If the outcome is HH, Lucy pays $3.

If the outcome is HT or TH, Lucy gets $2.

If the outcome is TT, Lucy pays $1.

The probability distribution of Lucy's profit is given below:

$\left|\begin{array}{c|c|c|c}$Profit(x)&-\$3&-\$1&\$2\\P(x)&1/4&1/4&2/4\end{array}\right|$

Expected Profit

$=(-3 \times \frac14)+(-1\times \frac14)+(2 \times \frac24)\\=$0$

Lucy's expected profit from the game is $0.

7 0

3 years ago

The brand manager for a brand toothpaste must plan a campaign designed to increase brand recognition. He wants to first determin

bulgar [2K]

We need to find out how many adults must the brand manager survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage.

From the given data we know that our confidence level is 90%. From Standard Normal Table we know that the critical level at 90% confidence level is 1.645. In other words, $Z_{Critical}=1.645$ .

We also know that E=5% or E=0.05

Also, since, $\hat{p}$ is not given, we will assume that $\hat{p}$ =0.5. This is because, the formula that we use will have $\hat{p}(1-\hat{p})$ in the expression and that will be maximum only when $\hat{p}$ =0.5. (For any other value of $\hat{p}$ , we will get a value less than 0.25. For example if, $\hat{p}$ is 0.4, then $1-\hat{p}=0.6$ and thus, $\hat{p}(1-\hat{p})=0.24$ .).