Question

Suppose that 65% of all adults regularly consume coffee, 60% regularly consume carbonated soda, and 75% regularly consume at least one of these two (a) What is the probability that a randomly selected adult regularly consumes both coffee and soda? 0.50 (b) What is the probablity that a randomly selected adult doesn't regularly consume at least one of these two products? 05 Need Help?

Answer 1

Let A be event that adults regularly consume coffee.

And B be event that adults regularly consume Soda.

Hence

P(A)= 0.65 and P(B)=0.60

Now we have 75% adults consume at least one of these products.

Means $\large P(A\cup B) = 0.75$

A)

$\large P(A \cap B) = P(A) + P(B) -P(A\cup B)$

$\large P(A\cap B) =$$\large 0.65+0.60-0.75 = 0.50$

Hence correct answed is 0.50

B) Now here probability that randomly selected adult doesn't regukregu consume at least one of these products .

I.e.

$\large {P(A \cup B)}'$ =​​​​​​$\large 1- P(A \cup B) = 1- 0.75$

=0.25

Hence correct answer is 0.25