Question

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suppose that 65% of all adults regularly consume coffee 40% regularly consume carbonated soda, and 35% regularly co sa res both cof en and sod. (a) What is the chance a randomly selected adult regularly drinks coffee but doesn't drink soda? (b) What is the probabity that a randomly selected adult consumes coffee, soda or both? (c) What ie the probability that a randomly selected adult doesn't regularly consume at least ons of these two products?

Answer 1

Let,

A : Event that adults regularly consume coffee.

P( A ) = 65% = 0.65

B: Event that adults regularly consume soda.

P( B ) = 40% = 0.4

P( A and B ) = 0.35

a)

Probability that a randomly selected adults regularly drink coffee but doesn't drink soda is,

= P( A ) - P( A and B )

=0.65 - 0.35

= 0.3

b)

Probability that a randomly selected adult consumes coffee, soda or both is,

P( A or B )= P( A ) + P( B ) - P( A and B )

P( A or B )= 0.65 + 0.40 - 0.35

P( A or B ) = 0.7

c)

Probability that a randomly selected adult doesn't consumes at least one of these two product is ,

P( A or B )^c = 1 - P( A or B )

P( A or B )^c = 1 - 0.7

P( A or B )^c = 0.3