Bluebook SAT Test Probability and Conditional Probability 12

Question 1

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

Accepted Answer

13/20

Answer

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.

Question 2

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

Accepted Answer

1/32

Answer

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

Question 3

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?

Accepted Answer

8/11

Answer

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

Question 4

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

Accepted Answer

0.18

Answer

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

Question 5

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?

Accepted Answer

1/8

Answer

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

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