In one town, 61% of adults have health insurance. What is the probability that 6 adults selected at random from the town all have health insurance?

The probability of both/all events occurring is found by multiplying the probabilities of the individual events.

.61^6 = ?

To find the probability that 6 adults selected at random from the town all have health insurance, we can use the concept of probability and the given information that 61% of adults in the town have health insurance.

First, let's calculate the probability of an individual adult having health insurance. Since 61% of adults in the town have health insurance, that means the probability of an individual adult having health insurance is 0.61 or 61% (expressed as a decimal).

Now, to find the probability that all 6 randomly selected adults have health insurance, we need to calculate the probability of one adult having insurance and then multiply it by itself six times (since there are six adults).

Using the multiplication rule, the probability that all six adults have health insurance is:

(Probability of one adult having health insurance) raised to the power of (number of adults selected)

P(6 adults with health insurance) = (0.61) ^ 6

Calculating this expression, we get:

P(6 adults with health insurance) ≈ 0.032243

Therefore, the probability that 6 adults selected at random from the town all have health insurance is approximately 0.032243, or about 3.22%.