Bayes' Theorem

You have two bags of candy, both with strawberry and lemon flavored pieces. Bag 1 has 4 lemon and 5 strawberry pieces. Bag 2 has 8 lemon and 7 strawberry pieces. You randomly choose a bag and then pick a candy. You choose a strawberry one. What’s the probability that it came from bag 2? Round your answer to 2 decimal places.

• 0.63

• 0.46

• 0.54

• 0.34

There are two unknown events, A and B. If B occurs first, what formula would find P(A)?

• 𝑃(𝐵) ∙ 𝑃(𝐴′|𝐵′) + 𝑃(𝐵′) ∙ 𝑃(𝐴′|𝐵′)

• 𝑃(𝐵) ∙ 𝑃(𝐴′|𝐵) + 𝑃(𝐵′) ∙ 𝑃(𝐴′|𝐵′)

• 𝑃(𝐵) ∙ 𝑃(𝐴|𝐵) + 𝑃(𝐵′) ∙ 𝑃(𝐴|𝐵′)

• 𝑃(𝐵′) ∙ 𝑃(𝐴|𝐵′) + 𝑃(𝐵′) ∙ 𝑃(𝐵|𝐴′)

The probability that you study for your History test is 80%. If you study, the probability of earning an A is 90%. If you don’t study, the probability of earning an A is 20%. You find out that you earned an A on the test. What’s the probability that you studied? Round your answer to the nearest hundredth.

• 0.95

• 0.80

• 0.85

• 0.99

The probability that it rains on a given day during the rainy season is 60%. If it’s raining, you’re late to school 30% of the time. If it’s not raining, you’re late 10% of the time. If you’re late to school, what’s the probability that it was raining? Round your answer to the nearest hundredth.

• 0.82

• 0.95

• 0.70

• 0.65

P( Sports Car | male)

Mathematical Equivalence

OFF

Match the following theoretical probabilities.

• Flipping a Coin

• Spinner with 8 Equal Sections

• Choosing from Red, Green, Yellow, or Blue

• Rolling a Die

• Rolling a 5 or 6 on a Die