Question

In a local car lot, 1/6

of the cars have standard transmissions. Find the

probability that 3 of 4 randomly-selected cars have standard transmissions.

Answer 1

Answer:
`(5)/(324)`

Explanation:

Given

Probability that car has a standard transmission is
`(1)/(6)`

So, the probability that the car does not have transmission is

`1-(1)/(6)=(5)/(6)`

Probability of that 3 out of 4 randomly selected cars have standard transmissions is given by selecting 3 cars with standard deviation and then multiply by their respective probabilities

`\Rightarrow P=^4C_3\cdot \left((1)/(6)\right)^3\cdot \left((5)/(6)\right)\\\\\Rightarrow P=4*(5)/(6^4)\\\\\Rightarrow P=(20)/(1296)\\\\\Rightarrow P=(5)/(324)`