100 PNTS AND BRAINLIST FOR CORRECT ANWSER WITH A GOOD EXPLAINATION!! You pay $10 to play the following game of chance. There is a bag containing 20 balls: five are red, five are green, and the rest are yellow. You are to draw one ball from the bag. You will win $18 if you draw a red ball, and you will win $10 if you draw a green ball. You win nothing for drawing a yellow ball. What is the expected value? Should you play?

your answer is 20

Step-by-step explanation:

Expert's answer

Because the events (draw a red/green/yellow ball) form the full group and do not intersect, we can calculate the expected win/lose for 1 game as

\mathbb{E}X = \sum\limits_k {{w_k}P(k)}EX=k∑wkP(k)

Where {P(k)}P(k) is a probability of the certain event, that can be calculated as P(k) = \frac{{{N_k}}}{N}P(k)=NNk where {N_k}Nk is the number of k-type balls and N = \sum\limits_k {{N_k}}N=k∑Nk is the amount of balls, {{w_k}}wk is the win/lose if we get the k-th type ball (it can be calculated as {w_k} = {x_k} - ywk=xk−y where {x_k}xk is the win for the k-th type ball and yy is the price for the 1 game). We get

\mathbb{E}X = \sum\limits_k {{w_k}P(k)} = \$4 \cdot \frac{5}{{12}} +\$ 2 \cdot \frac{4}{{12}} + \$( - 10) \cdot \frac{3}{{12}} = -\$ \frac{1}{6}EX=k∑wkP(k)=$4⋅125+$2⋅124+$(−10)⋅123=−$61

Then because the games are independent, the total result after 100 times is

\mathbb{E}Y = n \cdot \mathbb{E}X = - \$\frac{1}{6} \cdot 100 = - \$\frac{{50}}{3} \approx - \$16.667EY=n⋅EX=−$61⋅100=−$350≈−$16.667

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify