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 of the event that at least one of them enjoys drinking soda.
The complement of an event is the probability of it not happening. In this case, the complement event is that at least one adult enjoys drinking soda. Therefore, the probability of the complement event is 1 minus the probability of the original event (none of them enjoy drinking soda).
The probability that an individual adult does not enjoy drinking soda is 1 minus the given percentage, which is 100% - 65% = 35%.
Now, to find the probability that none of the 12 adults enjoy drinking soda, we multiply the probability of an individual adult not enjoying soda by itself 12 times, since the events are independent (assuming that the selection of adults is random and with replacement).
Probability of none enjoying soda = (Probability of an individual not enjoying soda)^12
= (0.35)^12
≈ 0.000064
Therefore, the probability that none of the 12 adults enjoy drinking soda is approximately 0.000064 or 0.0064%.