According to an Internet posting, 65% of adults enjoy drinking soda. Choose a group of 12 adults at random. The probability that none of them enjoy drinking soda is?
To find the probability that none of the 12 adults enjoy drinking soda, we need to calculate the complement probability.
The complement probability is the probability that the opposite event occurs, which in this case would be the probability that at least one of the 12 adults enjoys drinking soda.
To calculate the complement probability, we can subtract the probability of the opposite event from 1.
The probability that at least one of the 12 adults enjoys drinking soda is equal to 1 minus the probability that none of them enjoy it.
Given that 65% of adults enjoy drinking soda, the probability that one adult does not enjoy it is 1 - 0.65 = 0.35.
Since the selection is random, the probability that none of the 12 adults enjoy soda can be calculated using the formula for independent events:
P(none of them enjoy soda) = (0.35)^12
Calculating this:
P(none of them enjoy soda) = 0.0002142
So, the probability that none of the 12 adults enjoy drinking soda is approximately 0.0002142.