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Multiplication Rule Probability

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Multiplication Rule Probability

For each question, consider whether the events are independent or dependent. Show your calculations where asked. Give probabilities as fractions in simplest form unless another form is requested.

Multiplying Probabilities

1.A fair coin is tossed and a fair six-sided die is rolled. What is the probability of getting tails and rolling a 5?

1/12
1/8
1/6
1/3

2.For two independent events A and B, which calculation gives the probability that both events occur?

P(A) + P(B)
P(A) × P(B)
P(A) − P(B)
P(A) ÷ P(B)

3.A pouch holds 3 yellow counters and 5 purple counters. One counter is chosen, returned to the pouch, and then a second counter is chosen. What is the probability that both counters are yellow?

3/8
3/16
9/64
6/16

4.Select all that apply. More than one choice is correct: which pairs of events are independent?

Spin a fair spinner twice
Choose two books from a shelf without putting the first back
Roll a die, then toss a coin
Draw two cards from a deck without replacement

Work It Out

5.A spinner has 4 equal sectors: one orange, one blue, and two white. It is spun twice. Find the probability of landing on blue both times. Show your working.

6.A carton contains 7 oat biscuits and 4 ginger biscuits. Maia takes one biscuit and eats it, then takes another. What is the probability that both biscuits are oat? Show your working.

7.Complete the statement. For independent events A and B, P(A and B) = × .

8.Complete the statement. For dependent events, the probability of the second event on the outcome of the first event.

Probability in Context

9.A forecast gives a 40% chance of rain on Friday and a 30% chance on Saturday. If rain on the two days is assumed to be independent, what is the probability of rain on both days? Give your answer as a percentage.

10.Explain the difference between independent and dependent events. Give one suitable example of each.

11.A group has 10 boys and 14 girls. Two students are selected at random without replacement. Find the probability that both selected students are girls. Show your reasoning.