Question

General mills is testing 12 new cereals for possible production. They are testing 4 oat cereals, 3 wheat cereals, and 5 rice cereals. If each of the 12 cereals has the same chance of being produced, and 4 new cereals will be produced, determine the probability that of the 4 new cereals that will be produced, 1 is an oat cereal, 2 are wheat cereals, and 1 is a rice cereal?

Answer 1

The probability that 1 oat cereal, 2 wheat cereals, and 1 rice cereal will be produced out of the 4 new cereals is 5/33.

Step-by-step explanation:

To determine the probability that 1 oat cereal, 2 wheat cereals, and 1 rice cereal will be produced out of the 4 new cereals, we need to calculate the probability of each event separately and then multiply them together.

The probability of selecting 1 oat cereal out of 4 is 4/12, since there are 4 oat cereals out of the total 12 cereals being tested.

The probability of selecting 2 wheat cereals out of 3 is (3 choose 2) / (12 choose 4), which simplifies to 3/11.

The probability of selecting 1 rice cereal out of 5 is 5/10, since there are 5 rice cereals out of the remaining 10 cereals after selecting the oat and wheat cereals.

Now, we multiply these probabilities together: (4/12) * (3/11) * (5/10) = 60/396 = 5/33.

Therefore, the probability that of the 4 new cereals produced, 1 is an oat cereal, 2 are wheat cereals, and 1 is a rice cereal is 5/33.