Question

5/You spin the spinner

AND flip a coin. Find the
probability of the
compound events. Write
as a fraction and percent.

a) P(1 and tails) =
b) P(even and heads) = (The spinner is 1-5)

Answer 1

a) P(1 and tails) = 1/10 = .1

b) P(even and heads) = 1/5 = .2

Explanation:

The spinner has 5 outcomes: 1-5.

The coin has 2 outcomes: Heads or Tails.

We want to find the probability of P(1 ∩ T) and P(2,4 ∩ H).

a) P(1 and tails)

Spinning the spinner and flipping the coin are independent events; therefore, getting one outcome has no effect on the outcome of another.

For independent events, the multiplication rule is:

• P(A and B) = P(A) * P(B)

If we use this formula for A, we get that:

• P(1 and tails) = P(1) * P(tails)

The probability of getting a 1 on the spinner is P(1) = 1/5.

The probability of getting tails on the coin toss is P(tails) = 1/2.

We can now multiply these probabilities together:

• P(1 and tails) = 1/5 * 1/2 = 1/10

The probability of getting a 1 on the spinner and tails on the coin toss is P(1 and tails) = 1/10 or .1.

b) P(even and heads)

There are two even numbers between 1 and 5: 2 and 4.

The probability of getting an even number on the spinner is 2/5.

The probability of getting heads on the coin toss is 1/2.

We can multiply these probabilities together:

• P(even and heads) = 2/5 * 1/2 = 2/10 = 1/5

The probability of getting an even number on the spinner and heads on the coin toss is P(even and heads) = 1/5 or .2.