Question

There are 10 vehicles in a parking lot: 3 SUVs and 7 trucks. The probability that any 7 randomly chosen parking spots have 2 SUVs and 5 trucks or 3 SUVs and 4 trucks is____ . The probability that of any 7 randomly chosen vehicles, exactly 1 is an SUV is____ .

Answer 1

0.817 and 0.175

Step-by-step explanation:

Answer 2

The probability that any 7 randomly chosen parking spots have 2 SUVs and 5 trucks or 3 SUVs and 4 trucks is 49/60

The probability that of any 7 randomly chosen vehicles, exactly 1 is an SUV is = 7/40

Explanation:

probability of taking 7 vehicles from 10 vehicles = 10C₇

number of ways taking 2 SUVs and 5 trucks = 3C₂* 7C₅ = 63

number of ways taking 3 SUVs and 4 trucks =3C₁*7C₄ = 35

number of ways taking 2 SUVs and 5 trucks or 3 SUVs and 4 trucks = 63 + 35 = 98

The probability that any 7 randomly chosen parking spots have 2 SUVs and 5 trucks or 3 SUVs and 4 trucks is = 98/120 = 49/60

number of ways taking 7 randomly chosen vehicles, exactly 1 is an SUV = 3C₁*7C₆ = 21

The probability that of any 7 randomly chosen vehicles, exactly 1 is an SUV is 21/120 = 7/40