Compound probability Practice Questions (Grade 7)

Question 1easy

A meal has 3 mains and 4 sides. How many different (main, side) combinations are possible?

By the multiplication principle: $3 \times 4 = 12$ .

Question 2easy

For two independent events, the probability of flipping two heads in a row: $P(A)=\tfrac{1}{2}$ , $P(B)=\tfrac{1}{2}$ . Find $P(A \text{ and } B)$ as a simplified fraction.

Multiply: $P(A \text{ and } B) = \tfrac{1}{2} \times \tfrac{1}{2} = \tfrac{1}{4}$ .

Question 3easy

Two fair coins are flipped. How many outcomes are in the sample space?

Each coin has $2$ outcomes, so the sample space has $2 \times 2 = 4$ outcomes: HH, HT, TH, TT.

Question 4easy

For two independent events, the probability of rolling two 6's: $P(A)=\tfrac{1}{6}$ , $P(B)=\tfrac{1}{6}$ . Find $P(A \text{ and } B)$ as a simplified fraction.

Multiply: $P(A \text{ and } B) = \tfrac{1}{6} \times \tfrac{1}{6} = \tfrac{1}{36}$ .

Question 5easy

Mia can pick from $5$ shirts and $2$ hats. How many different (shirt, hat) outfits are possible?

By the counting principle: $5 \times 2 = 10$ .

Question 6easy

For two independent events, the probability of a head then a 4: $P(A)=\tfrac{1}{2}$ , $P(B)=\tfrac{1}{6}$ . Find $P(A \text{ and } B)$ as a simplified fraction.

Multiply: $P(A \text{ and } B) = \tfrac{1}{2} \times \tfrac{1}{6} = \tfrac{1}{12}$ .

Question 7easy

Two fair coins are tossed. What is the probability of getting exactly one head?

The sample space is HH, HT, TH, TT. Exactly one head appears in $2$ of the $4$ equally likely outcomes: $\dfrac{2}{4} = \dfrac{1}{2}$ .

Question 8easy

For two independent events, the probability of an even roll then a head: $P(A)=\tfrac{3}{6}$ , $P(B)=\tfrac{1}{2}$ . Find $P(A \text{ and } B)$ as a simplified fraction.

Multiply: $P(A \text{ and } B) = \tfrac{3}{6} \times \tfrac{1}{2} = \tfrac{1}{4}$ .

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