Question

it has been estimated that only about 13% 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)
part (e)
what is the probability that we must survey at least 5 california residents until we find a california resident who does not have adequate earthquake supplies? (round your answer to four decimal places.)

Explanation:

Step1: Define success probability

Let $p$ = probability a resident has adequate supplies = $0.15$.
We want the probability that the first 4 surveyed residents all have adequate supplies (since "at least 5" means the first 4 do NOT meet our target of finding someone without adequate supplies).

Step2: Calculate joint probability

The probability that 4 independent residents all have adequate supplies is $p^4$.
$$0.15^4 = 0.15 \times 0.15 \times 0.15 \times 0.15$$

Step3: Compute the final value

$$0.15^4 = 0.00050625$$
Round to four decimal places.

Answer:

0.0005