Stats word problem

Question

3. The probability that a person picked at random is over 65 years old is 0.12. If two people are picked at random, find the probability that:

a. they are both over 65


b. neither is over 65


c. at least one is over 65

Answer 1

PROBABILITY OF BOTH BEING OVER 65:

(0.12) × (0.12) gives 0.0144.

PROBABILITY OF NEITHER BEING OVER 65:

(1 − 0.12) × (1 − 0.12) gives (0.88)² or 0.7744.

PROBABILITY OF AT LEAST ONE BEING OVER 65:

(0.12)(0.88) + (0.88)(0.12) + (0.12)(0.12) gives 0.2256.

[In other words, simply take 1 − (0.7744 found above)

which again gives 0.2256.]

Note also that either nobody is over 65 or at least one person is over 65.

In accordance, the corresponding probabilities 0.7744 and 0.2256

found above sum to 1 which is the highest probability possible

(meaning there is "absolute certainty" that either nobody is over 65 or

at least one person is over 65).