Suppose that 60% of all adults regularly consume coffee, 40% regularly consume carbonated soda, and 75% regularlyconsume at least one of these two products.(a) What is the probability that a randomly selected adult regularly consumes both coffee and soda?(b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?

If A and B denotes two events, the probability PA∪B denotes the probability of happening of either…

Answered: Suppose that 60% of all adults…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.8: Probabilities Of Disjoint And Overlapping Events

Problem 2C

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Question

Suppose that 60% of all adults regularly consume coffee, 40% regularly consume carbonated soda, and 75% regularly
consume at least one of these two products.
(a) What is the probability that a randomly selected adult regularly consumes both coffee and soda?
(b) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?

Expert Solution

Step 1

If $A$ and $B$ denotes two events, the probability $P (A \cup B)$ denotes the probability of happening of either of the events. It can be given as $P (A \cup B) = P (A) + P (B) - P (A \cap B)$ .

where,

$P (A)$ and $P (B)$ be the individual probabilities of happening of event $A$ and event $B$ , respectively.
$P (A \cap B)$ be the probabilities of happening of both the events $A$ and $B$ , at the same time.

If $A$ denotes an event, then $A'$ denotes the compliment of event $A$ . The event $A'$ denotes the not happening of event $A$ . Therefore, it can be said that $P (A) + P (A') = 1$ .