Question

it has been estimated that only about 15% of california residents have adequate earthquake supplies. suppose we are interested in the number of california residents we must survey until we find a resident who does not have adequate earthquake supplies.
part (a)
part (b)
part (c)
part (d)
what is the probability that we must survey just 3 or 4 residents until we find a california resident who does not have adequate earthquake supplies? (round your answer to four decimal places.)
part (e)

Explanation:

Step1: Define success probability

Probability of not having supplies: $p = 1 - 0.15 = 0.85$
Probability of having supplies: $q = 0.15$

Step2: Calculate P(survey 3 people)

This means first 2 have supplies, 3rd does not:
$P(X=3) = q^2 \times p = (0.15)^2 \times 0.85$
$P(X=3) = 0.0225 \times 0.85 = 0.019125$

Step3: Calculate P(survey 4 people)

This means first 3 have supplies, 4th does not:
$P(X=4) = q^3 \times p = (0.15)^3 \times 0.85$
$P(X=4) = 0.003375 \times 0.85 = 0.00286875$

Step4: Sum the two probabilities

$P(X=3 \text{ or } X=4) = 0.019125 + 0.00286875$

Answer:

0.02199375, rounded to four decimal places: 0.0220