Probability and Conditional Probability Flashcards

A quality inspector finds that 3% of products are defective. If 4 products are tested independently, what is the probability that exactly 1 is defective?

Answer: 0.1128

C(4,1)(0.03)^1(0.97)^3 = 4(0.03)(0.912673) ≈ 0.1128.

The two-way table shows 400 employees by shift and error rate. 0 Errors 1+ Errors Day Shift 150 50 Night Shift 80 120 Given an employee made at least one error, what is the probability they work the night shift?

Answer: 12/17

1+ errors total = 50 + 120 = 170; P(night | error) = 120/170 = 12/17.

Events H and K are independent. P(H) = 0.6 and P(K) = 0.7. What is P(neither H nor K)?

Answer: 0.12

P(not H) × P(not K) = 0.4 × 0.3 = 0.12.

A bag contains 5 red, 4 white, and 1 blue marble. A marble is drawn at random. What is the probability it is NOT white?

Answer: 3/5

Non-white = 5 + 1 = 6 out of 10; P = 6/10 = 3/5.

Two events A and B satisfy P(A) = 0.5, P(B | A) = 0.4, and P(B | not A) = 0.2. What is P(B)?

Answer: 0.30

P(B) = P(B|A)P(A) + P(B|not A)P(not A) = 0.4(0.5) + 0.2(0.5) = 0.20 + 0.10 = 0.30.

The two-way table shows 350 gym members by membership type and class attendance. Attended Class No Class Premium 100 50 Basic 60 140 If a member attended a class, what is the probability they have a Premium membership?

Answer: 5/8

Class attendees = 100 + 60 = 160; P(Premium | attended) = 100/160 = 5/8.

A game show contestant guesses at random from 3 doors. Behind one door is a car and behind the other two are goats. After the contestant picks a door, the host opens a different door revealing a goat, and asks if the contestant wants to switch. If the contestant switches, what is the probability of winning the car?

Answer: 2/3

This is the Monty Hall problem: switching gives a 2/3 probability of winning.