In one town, 70% of adults have health insurance. What is the probability that 6 adults selected at random from the town all have health insurance
To find the probability that all 6 adults selected at random from the town have health insurance, we need to multiply the probability that each individual adult has health insurance.
Since 70% of adults in the town have health insurance, the probability that one individual adult has health insurance is 70% or 0.7.
Therefore, the probability that all 6 randomly selected adults have health insurance is:
0.7 * 0.7 * 0.7 * 0.7 * 0.7 * 0.7 = 0.7^6 = 0.1176 or 11.76%.
To find the probability that all 6 adults selected at random have health insurance, we can use the concept of independent events.
The probability of the first adult having health insurance is 70%, or 0.7. Since each adult is selected randomly and independently, the probability of the second adult also having health insurance is still 0.7.
Continuing this process for all 6 adults, the probability that each one has health insurance is simply 0.7 multiplied by itself 6 times.
Hence, the probability that all 6 adults have health insurance is:
0.7 * 0.7 * 0.7 * 0.7 * 0.7 * 0.7 = 0.117649, or approximately 11.77%.