Question

General mills is testing 13 new cereals for possible production. they are testing 6 oat​ cereals, 4 wheat​ cereals, and 3 rice cereals. if each of the 13 cereals has the same chance of being​ produced, and 3 new cereals will be​ produced, determine the probability that of the 3 new cereals that will be​ produced, 1 is an oat cereal​, 1 is a wheat cereal​, and 1 is a rice cereal. question content area bottom part 1 the probability is enter your response here. ​(type an integer or a simplified​ fraction.)

Answer 1

The probability that 1 of the 3 new cereals produced is an oat cereal, 1 is a wheat cereal, and 1 is a rice cereal is 36/143.

Step-by-step explanation:

To determine the probability that 1 of the 3 new cereals produced is an oat cereal, 1 is a wheat cereal, and 1 is a rice cereal, we can use the concept of combinations.

There are 6 oat cereals, 4 wheat cereals, and 3 rice cereals. To select 1 oat cereal out of 6, we have 6 possibilities. Similarly, for wheat cereals and rice cereals, we have 4 and 3 possibilities respectively.

So, the total number of ways to select 1 oat cereal, 1 wheat cereal, and 1 rice cereal is 6 x 4 x 3 = 72.

The total number of ways to select any 3 cereals out of the 13 available is given by the combination formula:

C(n, r) = n! / (r!(n-r)!), where n is the number of cereals and r is the number of cereals to be selected.

Using this formula, C(13, 3) = 13! / (3!(13-3)!) = 286.

Therefore, the probability that 1 of the 3 new cereals produced is an oat cereal, 1 is a wheat cereal, and 1 is a rice cereal is 72/286, which simplifies to 36/143.