Question

QUESTION 1

A game is played that costs $1. To play, you roll one six-sided die. If you roll a six, you win $5. What is the expected value of this game?

	a.	$0
	b.	$5
	c.	$0.50
	d.	$4.50

QUESTION 2

A class room contains 32 students, 11 of whom are female. If one student is randomly chosen from the room, what is the probability the student is female?

Round to the nearest thousandth.

1 points   

QUESTION 3

: If the probability of an event is 0.171, then the probability of the complement of this event would be ____

QUESTION 4

A jar contains 5 red marbles, 13 white marbles, 4 red gumballs, and 4 white gumballs. If one object is selected at random, and you notice it is red, what is the probability it is a gumball given that is one of the red things? Round to 3 decimal places

QUESTION 5

If there are 6 lefthanded people in a group of size 92, we would say the probability of randomly selecting a lefthander from the group is_______ (round to the third decimal place)

QUESTION 6

1. Which of the following could not be a probability?

   	a.	0.02
   	b.	0.99
   	c.	-0.25
   	d.	0.7321

QUESTION 7

What probability tells you will happen, on the average, if an event is carried out many times

	a.	simulation
	b.	the mean
	c.	the sample space
	d.	expected value

QUESTION 8

1. 
   On any random flip of the coin, the chanc of getting "heads" is the same as the chance of getting "tails". We would say the two events are

   	a.	equally likely
   	b.	a simulation
   	c.	not likely
   	d.	a sample

QUESTION 9

1. 
   Which of the following could not be a probability?

   	a.	0.0232
   	b.	1.32
   	c.	0.25
   	d.	0.84

QUESTION 10

1. 
   The set of all possible outcomes from an experiment is known as the

   	a.	sample
   	b.	expected value
   	c.	sample space
   	d.	simulation

QUESTION 11

1. 
   Two events which have no outcomes in common are said to be

   	a.	lonely
   	b.	random
   	c.	disjoint
   	d.	discrete

QUESTION 12

1. expected value:
   
   A jar contains
   23 $1 bills
   7 $5 bills
   5 $10 bills
   3 $20 bills
   2 $50 bills
   1 $100 bill
   Every day for one year (365 times) you get to randomly pick a bill from the jar (the jar is refilled after every pick). For the year, what is the expected value of the total money you have won?
   
   Round to the nearest dollar

QUESTION 13

1. d vs c 4:
   
   Which type of variable would one that measure how many licks it takes to get to the center of a Tootsie Pop?

   	a.	Discrete
   	b.	Continuous

QUESTION 14

Which type of variable would time be in an experiment that measures how long it takes to eat a Tootsie Pop?

	a.	Discrete
	b.	Continuous

QUESTION 15

A game is played that costs $1. To play, you roll one six-sided die. If you roll a six, you win $5. What is the expected value of this game?

	a.	$0
	b.	$5
	c.	$0.50
	d.	$4.50

Answer 1

Q1:

Expected Value (EV) is the probability weighted averages of all possible outcomes. i.e. for Expected Value , the Probability of each event outcome is multiplied by its value.

if P(X=x) is the probability of x outcome and n be the value associated with x outcome  , then EV =

Selected Number on dice (x)	Total Win Amount in $	P(X=x)	Win Amount * P(X=x)
1	-1	0.167	-0.167
2	-1	0.167	-0.167
3	-1	0.167	-0.167
4	-1	0.167	-0.167
5	-1	0.167	-0.167
6	5	0.167	0.833

Hence expected Value = EV = = P(1) * (-1) + P(2) * (-1) + P(3) * (-1) + P(4) * (-1) + P(5) * (-1) + P(6) * 5

Substituting probability of numbers from above table.

EV = -0.833 +0.833 = 0

Hence Correct answer is a. $0

Q2:

Total students count = 32 ,

Female students = 11 , Male students = Total students - Female students = 32 - 11 = 21

If one student is selected randomly , probability of him to be female = Total Females / Total students in class room.

P(Female) = 11 / 32 = 0.344

Hence probability of randomly selected student is female is 0.344.

Q3:

We know that compliment rule of probability stats that sum of probabilities of events and its compliment must be equal to 1.

Probability of given event = 0.171

So, the probability of compliment of event = 1 - 0.171 = 0.829

Hence , Probability of compliment of event is 0.829

Q4:

Total Red marbles = 5 , White Marbles = 13 , Red gumballs = 4 , White gumballs = 4.

Total Red items = Red marbles + Red gumballs = 5 + 4 = 9

The probability of randomly selected red item is gumball is ,

P(Gumball|Red) = Total Red Gumballs/ Total Red items in jar = 4/9 = 0.444