Question

Bobby is designing a simulation to answer the question below.If 21% of the customers at a restaurant order fish, what is the probability that the next 3 customers in a row will order fish?Which design using red marbles to represent customers who order fish is BEST for the simulation?A. randomly select 3 marbles from 1 red marble and 99 green marblesB. randomly select 3 marbles from 7 red marbles and 93 green marblesC. randomly select 3 marbles from 21 red marbles and 79 green marblesD. randomly select 3 marbles from 63 red marbles and 37 green marbles

Answer 1

The probability of the second customer ordering a fish is independent of the first customer.

So, if the events are independent, the probability that the next three customers in a row will order a fish is (P):

`P=P_1\cdot P_2\cdot P_3`

Where P1, P2, and P3 are the probabilities of the first, second, and third customer ordering a fish.

Substituting the values:

`\begin{gathered} P=0.21\cdot0.21\cdot0.21 \\ P=0.009261 \end{gathered}`

Answer: The probability is 0.009261 = 0.9261%.

To represent the situation using red marbles:

Given that from 100 customers, 21 prefer fish, it is asked to calculate the probability of 3 customers in a row prefer fish.

From the options, randomly selecting 3 marbles from 21 red marbles and 79 green marbles is the best option, since there are 21 red marbles and a total of 100 (21 + 79) marbles.

Answer: C.