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.)r a simplified fraction.)

Answer 1

The probability of selecting one cereal each from oat, wheat, and rice categories is 1/47 when 3 out of 13 cereals are chosen.

Step-by-step explanation:

To 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, we approach this as a combination probability problem. Because the selection of one type of cereal does not affect the availability of the other types, we can calculate the probability of each event happening separately and then multiply them together.

Firstly, the probability of selecting 1 oat cereal from 6 is 6/13. Secondly, after selecting one oat cereal, we have 12 cereals left, and we want to select 1 wheat cereal out of the remaining 4 wheat cereals, so the probability is 4/12. Thirdly, now we have 11 cereals left and want to select 1 rice cereal out of the remaining 3 rice cereals, with the probability being 3/11.

The overall probability is therefore (6/13) * (4/12) * (3/11), which simplifies to 6/286 or approximately 1 in 47.67. So, our final answer is 1/47.