Question

 

1. Suppose a raffle costs $4 to buy a ticket. there are 100 tickets and you buy one ticket. what is your expected winning if the following prizes are awarded: one first prize: $80 two second prizes of $40 twenty third prizes of $8

2. a student estimates that for each question of a ten question true/false test, he has about a 75% chance of getting the answer right. what are his chances of passing the test with a grade of 80 or better? Show the calculator input for your answer.

3. Mary is looking for someone with a change of $1. she estimates that each person she asks has a 25 probability of having the right change. what is the probability that Mary will have to ask at least four people in order to find one with the right change?

Answer 1

1) Let X = winning amount

Let's make table from the given information.

The formulae used on the above excel-sheet are as follows:

So expected win = 3.2

Net win = 3.2 - 4 = -0.8

So the expected loss is $0.80

2)  a student estimates that for each question of a ten question true/false test, he has about a 75% chance of getting the answer right. what are his chances of passing the test with a grade of 80 or better? Show the calculator input for your answer.

Suppose X = number of correct answer of the questions.

Therefore X follows binomial distribution with n = 10 and p = 0.75

So if the student correctly answer at least 8 questions then he/she pass the test.

So we need to find P( X >= 8) = 1 - P( X <= 7) ....( 1 )

Let's use TI-84 Plus calculator.

Command:

2ND >>> VARS >>> B:binomcdf( >>> Enter

trials : 10

p : 0.75

x value : 7

Paste ( highlight paste and then enter)

Again Enter

Then we get 0.4744

Plug this value in equation ( 1 ), we get

P( X >= 8) = 1 - 0.4744 = 0.5256 ( This is the answer of part 2).