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Conditional Probability Exploration

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Conditional Probability Exploration

Use the tables to investigate conditional probability. The phrase “given that” tells you which group to focus on: use that group as the denominator. Give probabilities as simplified fractions or percentages unless a question asks for a different form.

Canteen survey

Forty students were asked whether they bought lunch at the canteen and whether they chose a piece of fruit.

Students

Chose fruit

Did not choose fruit

Total

Bought canteen lunch

Did not buy canteen lunch

Total

1.Among students who bought canteen lunch, what is the probability that a student chose fruit? Show which total you used as the denominator.

2.A student is known to have chosen fruit. What is the probability that they bought canteen lunch? Give a simplified fraction.

3.What is the probability that a randomly selected student both bought canteen lunch and chose fruit? Give your answer as a percentage.

4.Cooper says, “The probability of choosing fruit, given that a student bought lunch, is the same as the probability of buying lunch, given that a student chose fruit.” Is Cooper correct? Explain using the table.

Checking a weather forecast

Tahnee compared a forecast app with the observed weather over 100 days. The table records how often it rained and what the app predicted.

Forecast

It rained

It did not rain

Total

Rain predicted

No rain predicted

Total

100

5.On a day when the app predicted rain, what was the probability that it actually rained? Give a simplified fraction and a percentage.

6.On a day when it actually rained, what was the probability that the app had predicted rain? Give a simplified fraction.

7.Hamish claims the app was correct on 75% of the days. Use the table to check his claim and calculate the actual percentage of correct forecasts.

8.A forecast predicts no rain. Choose the correct probability that it will actually stay dry.

45/50 = 90%
45/65, about 69%
45/100 = 45%
20/50 = 40%

9.In your own words, explain how the denominator changes between “the probability of rain, given a rain forecast” and “the probability of a rain forecast, given that it rained.” Use the weather table in your explanation.