Question

general mills is testing 12 new cereals for possible production. 5 oats, 3 wheat and 4 rice cereals. if each 12 are produced the same and 4 new cereals are being produced the same determine the probability that 4 new cereals will be produced and 2 are oats and 2 are rice.

Answer 1

From the given information, the probability that 4 new cereals will be produced and 2 are oats and 2 are rice is

$P(2\text{oats }\cap\text{ 2 rice)}=P(2\text{oats)}\times P(2rice)$

The first probability is given by

$P(2\text{oats)}=\frac{5C2}{12C4}$

where 5C2 denotes the combination of 5 oats taken in 2. The second probability is given by

$P(2\text{rice)}=\frac{4C2}{12C4}$

Then the searched probability is

$\begin{gathered} P(2\text{oats }\cap\text{ 2 rice)}=P(2\text{oats)}\times P(2rice) \\ P(2\text{oats }\cap\text{ 2 rice)}=\frac{5C2}{12C4}\times\frac{4C2}{12C4} \end{gathered}$

which gives

$\begin{gathered} P(2\text{oats }\cap\text{ 2 rice)}=\frac{10}{495}\times\frac{6}{495} \\ P(2\text{oats }\cap\text{ 2 rice)}=0.00024 \end{gathered}$

then the answer is 0.00024.