At a vending machine, 6/11 people select a cola soda. Find the probability
that all of the next 3 people select a cola soda.
(6/11)^3
To find the probability that all of the next 3 people select a cola soda, we can use the concept of conditional probability.
Conditional probability represents the probability of an event happening given that another event has already occurred. In this case, the event that has already occurred is that 6/11 people have selected a cola soda.
The probability that the first person selects a cola soda is 6/11. Since we're looking for the probability that all of the next 3 people select a cola soda, we need to consider the probability for each person in this scenario.
Given that the first person already selected a cola soda, the probability that the second person selects a cola soda is 5/10, since there are now only 5 cola sodas left out of 10 choices.
Similarly, given that the first two people have selected cola sodas, the probability that the third person selects a cola soda is 4/9, because there are now only 4 cola sodas left out of 9 choices.
To find the probability of all three events occurring together, we multiply their individual probabilities:
(6/11) * (5/10) * (4/9) = 120/990 ≈ 0.1212
Therefore, the probability that all of the next 3 people select a cola soda is approximately 0.1212.