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Chapter 2: Q14E (page 65)

Suppose that 55% of all adults regularly consume coffee,45% regularly consume carbonated soda, and 70% 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鈥檛 regularly consume at least one of these two products?

Short Answer

Expert verified

a. The probability that a randomly selected adult regularly consumes both coffee and soda is 0.30

b. The probability that a randomly selected adult doesn鈥檛 regularly consume at least one of these two products is 0.30

Step by step solution

01

Given information

The probability that all adults regularly consume coffee is 0.55.

The probability that adults regularly consume carbonated soda is 0.45.

The probability that the adults regularly consume at least one of the two products is 0.70

02

Compute the probability

Let A be the event representing that all adults regularly consume coffee.

Let B be the event representing that adults regularly consume carbonated soda.

The probabilities from the provided information are,

\(\begin{aligned}P\left( A \right) = 0.55\\P\left( B \right) = 0.45\\P\left( {A \cup B} \right) = 0.70\end{aligned}\)

a.

The probability that a randomly selected adult regularly consumes both coffee and soda is computed as,

\(\begin{aligned}P\left( {A \cap B} \right) &= P\left( A \right) + P\left( B \right) - P\left( {A \cup B} \right)\\ &= 0.55 + 0.45 - 0.70\\ &= 0.30\end{aligned}\)

Therefore, the probability that a randomly selected adult regularly consumes both coffee and soda is 0.30.

b.

The probability that a randomly selected adult doesn鈥檛 regularly consume at least one of these two products is computed as,

\(\begin{aligned}P\left( {A \cup B} \right)' &= 1 - P\left( {A \cup B} \right)\\ &= 1 - 0.70\\ &= 0.30\end{aligned}\)

Therefore, the probability that a randomly selected adult doesn鈥檛 regularly consume at least one of these two products is 0.30.

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