A school survey found that 9 out of 10 students like pizza. If three students are chosen at random with replacement, what is the probability that all three students like pizza? Answer with 3 decimal places.
0.729
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events (9/10).
To find the probability that all three students like pizza, we need to compute the probability of each student liking pizza and then multiply them together.
Given that the survey found that 9 out of 10 students like pizza, the probability of any individual student liking pizza is 9/10 or 0.9.
Since we are choosing three students at random with replacement, the probability of each student liking pizza remains 0.9 for each selection.
To find the probability that all three students like pizza, we multiply the probabilities together:
P(liking pizza for all 3 students) = P(liking pizza for the 1st student) * P(liking pizza for the 2nd student) * P(liking pizza for the 3rd student)
= 0.9 * 0.9 * 0.9
Calculating this expression:
0.9 * 0.9 * 0.9 = 0.729
Therefore, the probability that all three students like pizza is 0.729 or 0.729 (rounded to 3 decimal places).
To find the probability that all three students like pizza, we need to calculate the probability of each individual student liking pizza, and then multiply these probabilities together since the events are independent.
Given that 9 out of 10 students like pizza, the probability that any individual student likes pizza is 9/10 = 0.9.
Since the students are chosen with replacement, the probability remains the same for each selection.
To find the probability of all three students liking pizza, we multiply the probabilities together:
0.9 * 0.9 * 0.9 = 0.729
Therefore, the probability that all three students selected like pizza is 0.729.