Answer: [tex]\dfrac{5}{324}[/tex]
Step-by-step explanation:
Given
Probability that car has a standard transmission is [tex]\frac{1}{6}[/tex]
So, the probability that the car does not have transmission is
[tex]1-\dfrac{1}{6}=\dfrac{5}{6}[/tex]
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
[tex]\Rightarrow P=^4C_3\cdot \left(\dfrac{1}{6}\right)^3\cdot \left(\dfrac{5}{6}\right)\\\\\Rightarrow P=4\times\dfrac{5}{6^4}\\\\\Rightarrow P=\dfrac{20}{1296}\\\\\Rightarrow P=\dfrac{5}{324}[/tex]
