Answer:
B. 0.175
Step-by-step explanation:
We are given that,
Total number of vehicles = 10
Number of SUV = 3
Number of trucks = 7
Probability to select any random 7 vehicles out of 100 is [tex]\binom{10}{7}[/tex].
It is required to select exactly 1 SUV.
Thus, we have, out of the 7 vehicles, exactly 1 is a SUV and other 6 are trucks.
So, the probability of selecting exactly 1 SUV is [tex]\frac{\binom{3}{1}\times \binom{7}{6}}{\binom{10}{7}}[/tex]
i.e. Required probability = [tex]\frac{3\times 7}{\frac{10\times 9\times 8}{6}}[/tex]
i.e. Required probability = [tex]\frac{3\times 7}{10\times 3\times 4}[/tex]
i.e. Required probability = [tex]\frac{21}{120}[/tex]
i.e. Required probability = 0.175
Hence, the probability to randomly select exactly 1 SUV from 7 vehicles is 0.175
