Question

In: Statistics and Probability

The college hiking club is having a fund raiser to buy new equipment for fall and...

The college hiking club is having a fund raiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $1 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of the dinner for two at a local Chinese restaurant. The dinner is valued at $35. Since the fortune cookies were donated to the club, we can ignore the cost of the cookies. The club sold 701 cookies before the drawing.

(a) Lisa bought 22 cookies. What is the probability she will win the dinner for two? (Round your answer to three decimal places.)


What is the probability she will not win? (Round your answer to three decimal places.)


(b) Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? (Round your answer to two decimal places.)
$   

How much did she effectively contribute to the hiking club? (Round your answer to two decimal places.)
$

Solutions

Expert Solution

a) As there is only 1 winning number out of the 701 cookies sold, therefore there have to be 700 non winning numbers and 1 winning number

The probability that she will win the dinner is computed here as:

= Number of ways to select 1 winning ticket out of the winning ticket * Probability that rest 21 tickets are picked from the 700 non winning tickets / Total number of ways to select 22 tickets from 701 tickets

Therefore 0.031 is the required probability here.

Now the probability that she will not win is computed as:

= 1 - Probability that she will win

= 1 - 0.031

= 0.969

Therefore 0.969 is the required probability here.

b) The expected earnings for Lisa could be computed here as:

= 35* Probability that she will win

= 35* 0.031

= $1.10

Therefore $1.10 are Lisa's expected earnings here.

Now The effective contribution to the hiking club here is computed as:

= Cost of 22 tickets - Expected earnings

= 22*1 - 1.10

= $20.90

Therefore $20.90 is the effective contribution made by here.

orchestra answered 1 year ago
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