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)}* P(2rice)`

The first probability is given by

`P(2\text{oats)}=(5C2)/(12C4)`

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

`P(2\text{rice)}=(4C2)/(12C4)`

Then the searched probability is

`\begin{gathered} P(2\text{oats }\cap\text{ 2 rice)}=P(2\text{oats)}* P(2rice) \\ P(2\text{oats }\cap\text{ 2 rice)}=(5C2)/(12C4)*(4C2)/(12C4) \end{gathered}`

which gives

`\begin{gathered} P(2\text{oats }\cap\text{ 2 rice)}=(10)/(495)*(6)/(495) \\ P(2\text{oats }\cap\text{ 2 rice)}=0.00024 \end{gathered}`

then the answer is 0.00024.