Probability and Conditional Probability Flashcards

A survey of 500 adults found that 200 exercise daily and 300 do not. Of those who exercise daily, 160 have no chronic illness; of those who do not, 150 have no chronic illness. What is the probability a randomly selected adult exercises daily, given they have no chronic illness?

Answer: 16/31

No chronic illness = 160 + 150 = 310; P(exercise | no illness) = 160/310 = 16/31.

Two fair dice are rolled. What is the probability the product of the two numbers is 12?

Answer: 1/9

Pairs whose product is 12: (2,6),(3,4),(4,3),(6,2) — 4 outcomes out of 36; P = 4/36 = 1/9.

The two-way table shows 450 passengers by travel class and on-time status. On Time Delayed First Class 90 60 Economy 180 120 Are travel class and on-time status independent? Use the data to check.

Answer: Yes, because P(First Class) × P(On Time) = P(First Class and On Time)

P(on time | First) = 90/150 = 0.6; P(on time | Economy) = 180/300 = 0.6 — equal, so the events are independent.

A bag holds tiles labeled A, B, C, D, and E. Two tiles are drawn without replacement. What is the probability of drawing A first and B second?

Answer: 1/20

P = (1/5)(1/4) = 1/20.

Events F and G are independent with P(F) = 0.4 and P(F or G) = 0.7. What is P(G)?

Answer: 0.50

P(F or G) = P(F) + P(G) − P(F)P(G) → 0.7 = 0.4 + P(G) − 0.4P(G) → 0.3 = 0.6P(G) → P(G) = 0.5.

In a school of 400 students, 200 are in Grade 11 and 200 in Grade 12. Of the Grade 11 students, 80 are in the honor roll; of Grade 12 students, 100 are. What is the probability a randomly selected honor-roll student is in Grade 12?

Answer: 5/9

Honor roll total = 80 + 100 = 180; P(Grade 12 | honor roll) = 100/180 = 5/9.

A spinner has 10 equal sections: 4 red, 3 blue, 2 green, and 1 yellow. What is the probability of landing on blue or green in one spin?

Answer: 1/2

Blue + green = 3 + 2 = 5 out of 10; P = 5/10 = 1/2.