Question

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’t regularly consume at least one of these
two products?

Answer 1

Answer:

Step 1

Let A be the event that an adult Let B be the event that an adult consumes carbonated soda.

consumes coffee.

Given probabilities of the events.

P(A) = 0.55

P (B) = 0.45 P(AUB) = 0.7

Step 2: (a) Probability of consuming both coffee and soda

The case is intersection of event A and B, when a person drinks both coffee and soda.

P(ANB) = P(A) + P (B) –

= 0.55 +0.45 - 0.7

= 0.3

P (AUB)

P(ANB) = 0.3

Step 3: (b)

The given case represents compliment of the event when the adult consumes at least one of the drink. According to probability axiom, the probability is given by:

P ((AUB)') = 1 - P (AUB) = 1-0.7 = 0.3

Therefore,

P ((AUB)) = 0.3