Probability and Conditional Probability Flashcards

From the integers 1–20, one is chosen at random. What is the probability it is either odd or a multiple of 6?

Answer: 13/20

Odd: 1,3,5,7,9,11,13,15,17,19 (10); Multiples of 6: 6,12,18 (3); Overlap (odd multiples of 6): none; Union = 13; P = 13/20.

A student guesses on 5 true/false questions. What is the probability of answering all 5 correctly?

Answer: 1/32

P = (1/2)^5 = 1/32.

The two-way table shows 480 shoppers by age and purchase type. Online In-Store Under 40 180 60 40 and over 80 160 Given a shopper buys in-store, what is the probability they are 40 or over?

Answer: 8/11

In-store total = 60 + 160 = 220; P(40+ | in-store) = 160/220 = 8/11.

Events C and D satisfy P(C) = 0.3, P(D | C) = 0.6. What is P(C and D)?

Answer: 0.18

P(C and D) = P(C) × P(D | C) = 0.3 × 0.6 = 0.18.

In a deck of 40 cards numbered 1–40, one card is drawn at random. What is the probability the number is a multiple of 7?

Answer: 1/8

Multiples of 7 in 1–40: 7,14,21,28,35 — 5 numbers; P = 5/40 = 1/8.

A bag contains 8 tiles: 2 red, 3 blue, and 3 green. Two tiles are drawn at random without replacement. What is the probability the first is red and the second is green?

Answer: 3/28

P = (2/8)(3/7) = 6/56 = 3/28.

Of 200 commuters, 90 take the bus and 80 take the train, with 20 taking both. What is the probability a randomly chosen commuter takes neither?

Answer: 1/4

Bus or train = 90 + 80 − 20 = 150; neither = 200 − 150 = 50; P = 50/200 = 1/4.