Solved Examples and Worksheet for Probabilities of Compound Events

Q1There are 7 pastries, 6 burgers, and 2 pizzas in a restaurant. If Brad has money to buy only one item, then what is the probability of Brad selecting a burger?
A. 716
B. 12
C. 715
D. 25

Solutions
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Step: 1
Number of favorable outcomes = Number of burgers = 6
Step: 2
Number of possible outcomes = Total number of items in the restaurant = 7 + 6 + 2 = 15
  [Add the values.]
Step: 3
P(burger) = Number of favorable outcomesNumber of possible outcomes
Step: 4
= 615 = 25
  [Substitute and simplify.]
Step: 5
The probability of Brad selecting a burger is 25.
Correct Answer is :   25
Q2Find the value of the expression k/(x - y)2, if k = - 4, x = 3 and y = - 3.

A. 16
B. 19
C. - 19
D. 112

Solutions
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Step: 1
k(x - y)2
  [Original expression.]
Step: 2
= - 4(3 - (-3))2
  [Substituting.]
Step: 3
= - 462
  [Simplify inside the square brackets of the denominator.]
Step: 4
= - 19
  [Simplify.]
Step: 5
The value of the expression is - 19.
Correct Answer is :   - 19
Q3If you choose a medal at random, then what is the probability that you choose a gold medal?

A. 17
B. 12
C. 14
D. 18

Solutions
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Step: 1
Number of different ways of choosing a medal = (Number of ways of choosing a category) x (Number of ways of choosing a team) × (Number of ways of choosing a medal)
Step: 2
= 2 × 2 × 2 = 8
  [Substitute and multiply.]
Step: 3
P(gold medal) = Number of favorable outcomes / Total number of possible outcomes
Step: 4
Number of favorable outcomes = Number of gold medals given = 4
Step: 5
Total number of possible outcomes = Number of ways of choosing a medal = 8
Step: 6
= 48 = 12
  [Substitute and simplify.]
Step: 7
Probability of choosing a gold medal is 12.
Correct Answer is :   12
Q4Use a tree diagram to find the probability of choosing a red colored shirt of small size among red and green shirts of four sizes, s, l, m and xl.
A. 16
B. 17
C. 19
D. 18

Solutions
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Step: 1
Draw a tree diagram to find the sample space.
Step: 2
Number of possible outcomes is 8.
  [Red shirt of small, medium, large and extra large size and green shirt of large, small, medium and extra large size.]
Step: 3
Number of favorable outcomes = 1
  [Red shirt of small size.]
Step: 4
Probability (choosing a red colored shirt of small size) = Number of favorable outcomesNumber of possible outcomes = 18.
Step: 5
So, the probability of choosing a red colored shirt of small size is 18.
Correct Answer is :   18
Q5Use the tree diagram and find the probability of choosing a thick crust pizza with cheese topping among peppers, onions, cheese and mushroom toppings and thick and thin crusts.
A. 116
B. 18
C. 12
D. 14

Solutions
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Step: 1
Draw a tree diagram
Step: 2
In a tree diagram there are 8 different branches representing 8 possible outcomes.
Step: 3
There is only one favorable outcome for choosing a cheese pizza with thick crust.
Step: 4
P (Event) = number of favorable outcomes / number of possible outcomes.
  [Formula.]
Step: 5
P (Cheese pizza with thick crust) = 18
  [Substitute the values.]
Step: 6
So, the probability of choosing a cheese pizza with thick crust is 18.
Correct Answer is :   18
Q6The table shows the number of students in a class with brown and blue eyes. Two students are selected at random. What is the probability that both are with blue eyes?


A. 81361
B. 656703
C. 153703
D. 919

Solutions
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Step: 1
From the given table, Number of students with brown eyes = 12 + 8 = 20
Step: 2
Number of students with blue eyes = 7 + 11 = 18
Step: 3
Total number of students = 12 + 8 + 7 + 11 = 38
Step: 4
The number of ways of selecting 2 students with blue eyes from 18 students = 18C2
Step: 5
= 18!(18 - 2)! 2! = 18 × 17 × 16!16! × 2
  [nCr = n!(n - r)! r!.]
Step: 6
= 153
Step: 7
The total number of ways of selecting 2 students with blue eyes from 38 students = 38C2
Step: 8
= 38!(38 - 2)! 2! = 38 × 37 × 36!36! × 2
  [nCr = n!(n - r)! r!.]
Step: 9
= 703
Step: 10
The number of ways of selecting two students with blue eyes = 153703
  [Using the formula, number of favorable outcomestotal number of possible outcomes .]
Correct Answer is :   153703
Q7Kim wants to pull out a DVD or a CD from a box containing both. His choices are a DVD or a CD, audio or video, French or English. The tree diagram shows the possible outcomes of Kim choosing a DVD or a CD. What is the probability of Kim selecting a french audio DVD?

A. 16
B. 18
C. 14
D. 17

Solutions
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Step: 1
Total number of possible outcomes = 2 x 2 x 2 = 8
  [Use the counting principle.]
Step: 2
P(French audio DVD) = Number of favorable outcomesTotal number of possible outcomes
Step: 3
= 18
  [Substitute.]
Step: 4
Probability of selecting a French audio DVD is 18.
Correct Answer is :   18
Q8A coin is tossed 3 times. What is the probability of getting at least one tail?
A. 78
B. 18
C. 3132
D. one

Solutions
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Step: 1
To find the probability of getting at least one tail, it is easier to first find the probability of getting all heads and then taking its complement.
Step: 2
P(atleast one tail) = 1 - P(all heads)
  [P(E¯) = 1 - P(E).]
Step: 3
P(all heads) = (12)3 = 18
Step: 4
P(atleast one tail) = 1 - P(all heads) = 1 - 18= 78
Step: 5
The probability of getting atleast one tail when a coin is tossed 3 times is 78.
Correct Answer is :   78
Q9Use the tree diagram to find the number of ways in which Tony can choose a balloon.


A. 3
B. 2
C. 9
D. 6

Solutions
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Step: 1
A tree diagram displays all the possible choices where each branch represents a choice.
Step: 2
In the tree diagram, there are 9 different branches representing different choices available.
Step: 3
So, there are 9 different ways in which Tony can choose a balloon.
Correct Answer is :   9
Q10Michael wants to order a pizza. The tree diagram shows the different combinations that Michael can order a pizza. What is the probability of ordering thick crust pizza with mushroom topping?

A. 14
B. 17
C. 18
D. 16

Solutions
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Step: 1
Total number of possible outcomes = 4
  [Use the tree diagram.]
Step: 2
P(Thick Crust Pizza with Mushroom topping) = Number of favorable outcomes / Total number of possible outcomes
Step: 3
= 14
  [Substitute.]
Step: 4
Probability of ordering Thick Crust Pizza with Mushroom topping is 14.
Correct Answer is :   14
Q11There are 4 pink and 6 white balls in a bag. If two balls are drawn one after the other, then what is the probability of getting a pink ball first and white ball next, if the first ball drawn is replaced?
A. 47
B. 37
C. 17
D. 625

Solutions
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Step: 1
The two events, getting a pink ball first and a white ball next are independent events because the first ball drawn is replaced.
Step: 2
P (getting a pink ball first) = Number of pink ballsTotal number of balls = 410
Step: 3
P (getting a white ball next) = Number of white ballsTotal number of balls = 610
Step: 4
P (getting pink ball first and white next) = P (getting a pink ball first) × P (getting a white ball next) = 410 × 610 = 24100
  [Substitute and simplify the fraction.]
Step: 5
So, the probability of getting pink ball first and white ball next is 625.
Correct Answer is :   625

HighSchool Math