Givenn=4and probability of selecting a luxury vehicle=25% (a)Find the probality exactly 2 luxury vehicle will be chosen b) Find the probability at least 2 luxury vehicle will be chosen

(a)
1. Calculate the binomial coefficient for selecting exactly 2 luxury vehicles from 4:
\binom{4}{2} = \frac{4!}{2!(4-2)!} = 6
2. Calculate the probability to choose 2 luxury vehicles:
\binom{4}{2} \cdot (0.25)^2 \cdot (0.75)^2 = 6 \cdot 0.0625 \cdot 0.5625 = 0.2109375

Answer: 0.2109375

(b)
1. Calculate the probability to choose at least 2 luxury vehicles:
P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)
2. Calculate each term:
P(X = 2) = 0.2109375
P(X = 3) = \binom{4}{3} \cdot (0.25)^3 \cdot (0.75)^1 = 4 \cdot 0.015625 \cdot 0.75 = 0.046875
P(X = 4) = \binom{4}{4} \cdot (0.25)^4 \cdot (0.75)^0 = 1 \cdot 0.00390625 \cdot 1 = 0.00390625
3. Summarize the results to get the total probability:
0.2109375 + 0.046875 + 0.00390625 = 0.26171875

Answer: 0.26171875