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) = N u m b e r o f f a v o r a b l e o u t c o m e s N u m b e r o f p o s s i b l e o u t c o m e s

Step: 4

= 6 15 = 2 5

[Substitute and simplify.]

Step: 5

The probability of Brad selecting a burger is 2 5 .

Correct Answer is : 2 5

Step: 1

[Original expression.]

Step: 2

= - 4 ( 3 - ( - 3 ) ) 2

[Substituting.]

Step: 3

= - 4 6 2

[Simplify inside the square brackets of the denominator.]

Step: 4

= - 1 9

[Simplify.]

Step: 5

The value of the expression is - 1 9 .

Correct Answer is : - 1 9

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

= 4 8 = 1 2

[Substitute and simplify.]

Step: 7

Probability of choosing a gold medal is 1 2 .

Correct Answer is : 1 2

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) = N u m b e r o f f a v o r a b l e o u t c o m e s N u m b e r o f p o s s i b l e o u t c o m e s
= 1 8 .

Step: 5

So, the probability of choosing a red colored shirt of small size is 1 8 .

Correct Answer is : 1 8

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) = 1 8

[Substitute the values.]

Step: 6

So, the probability of choosing a cheese pizza with thick crust is 1 8 .

Correct Answer is : 1 8

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 = 1 8 C 2

Step: 5

= 1 8 ! ( 1 8 - 2 ) ! 2 ! = 1 8 × 1 7 × 1 6 ! 1 6 ! × 2

[n C r = n ! ( n - r ) ! r ! .]

Step: 6

= 153

Step: 7

The total number of ways of selecting 2 students with blue eyes from 38 students = 3 8 C 2

Step: 8

= 3 8 ! ( 3 8 - 2 ) ! 2 ! = 3 8 × 3 7 × 3 6 ! 3 6 ! × 2

[n C r = n ! ( n - r ) ! r ! .]

Step: 9

= 703

Step: 10

The number of ways of selecting two students with blue eyes = 1 5 3 7 0 3

[Using the formula, n u m b e r o f f a v o r a b l e o u t c o m e s t o t a l n u m b e r o f p o s s i b l e o u t c o m e s .]

Correct Answer is : 153 703

Step: 1

Total number of possible outcomes = 2 x 2 x 2 = 8

[Use the counting principle.]

Step: 2

P(French audio DVD) = N u m b e r o f f a v o r a b l e o u t c o m e s T o t a l n u m b e r o f p o s s i b l e o u t c o m e s

Step: 3

= 1 8

[Substitute.]

Step: 4

Probability of selecting a French audio DVD is 1 8 .

Correct Answer is : 1 8

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) = ( 1 2 ) 3 = 1 8

Step: 4

P(atleast one tail) = 1 - P(all heads) = 1 - 1 8 = 7 8

Step: 5

The probability of getting atleast one tail when a coin is tossed 3 times is 7 8 .

Correct Answer is : 7 8

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

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

= 1 4

[Substitute.]

Step: 4

Probability of ordering Thick Crust Pizza with Mushroom topping is 1 4 .

Correct Answer is : 1 4

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) = N u m b e r o f p i n k b a l l s T o t a l n u m b e r o f b a l l s = 4 10

Step: 3

P (getting a white ball next) = N u m b e r o f w h i t e b a l l s T o t a l n u m b e r o f b a l l s = 6 10

Step: 4

P (getting pink ball first and white next) = P (getting a pink ball first) × P (getting a white ball next) = 4 10 × 6 10 = 24 100

[Substitute and simplify the fraction.]

Step: 5

So, the probability of getting pink ball first and white ball next is 6 25 .

Correct Answer is : 6 25

- Probability of an Event Represented by a Number From 0 to 1-Gr 7-Solved Examples
- Possible Outcomes-Gr 7-Solved Examples
- Identifying Equally Likely Outcomes-Gr 7-Solved Examples
- Likelihood of an Event-Gr 7-Solved Examples
- Making Predictions-Gr 7-Solved Examples
- Making Inferences from Data of Two Populations-Gr 7-Solved Examples

- Event