Probability and Conditional Probability Flashcards

A two-way table records 500 households by internet speed and streaming usage. Streams Daily Does Not Stream High-speed internet 180 70 Low-speed internet 60 190 What is the probability a household streams daily?

Answer: 12/25

Total streaming = 180 + 60 = 240 out of 500; P = 240/500 = 12/25.

P(A) = 0.7. If A and B are independent and P(A and B) = 0.28, what is P(B)?

Answer: 0.40

P(B) = P(A and B)/P(A) = 0.28/0.7 = 0.40.

Three cards labeled 1, 2, and 3 are shuffled. Two cards are drawn one at a time without replacement. What is the probability the sum of the two cards equals 4?

Answer: 1/3

Ordered pairs summing to 4: (1,3) and (3,1); total ordered pairs = 3×2 = 6; P = 2/6 = 1/3.

A store's records show that 60% of customers buy clothing, 40% buy accessories, and 20% buy both. What is the probability a customer buys clothing but NOT accessories?

Answer: 2/5

Clothing only = 0.60 − 0.20 = 0.40 = 2/5.

The two-way table shows 360 athletes by sport and injury history. Injured No Injury Contact 90 60 Non-contact 50 160 What is the probability a randomly selected athlete is in a contact sport, given they have no injury?

Answer: 3/11

No injury total = 60 + 160 = 220; contact, no injury = 60; P = 60/220 = 3/11.

A bucket holds 8 balls: 3 orange and 5 gray. Three balls are drawn one at a time with replacement. What is the probability all three are gray?

Answer: 125/512

P(gray) = 5/8; with replacement, P(all gray) = (5/8)³ = 125/512.

In a school of 800 students, 480 play at least one sport. If a student is chosen at random, what is the probability the student plays NO sports?

Answer: 2/5

No sports = 800 − 480 = 320; P = 320/800 = 2/5.