Answer:
The approximate probability that Kevin chose to get home from work by bus, given that he arrived home after 7 pm = 0.838
Step-by-step explanation:
Let the probability that Kevin arrives home after 7 pm be P(L)
Probability that Kevin uses the bus = P(B)
Probability that Kevin uses the car = P(C)
Probability of arriving home after 7 pm if the car was taken = P(L|C) = 4% = 0.04
Probability of arriving home after 7 pm if the bus was taken = P(L|B) = 15% = 0.15
The bus is cheaper, So, he uses the bus 58% of the time.
P(B) = 58% = 0.58
P(C) = P(B') = 1 - P(B) = 1 - 0.58 = 0.42
The approximate probability that Kevin chose to get home from work by bus, given that he arrived home after 7 pm = P(B|L)
The conditional probability P(A|B) is given mathematically as
P(A|B) = P(A n B) ÷ P(B)
Hence, the required probability, P(B|L) is given as
P(B|L) = P(B n L) ÷ P(L)
But we do not have any of P(B n L) and P(L)
Although, we can obtain these probabilities from the already given probabilities
P(L|C) = 0.04
P(L|B) = 0.15
P(B) = 0.58
P(C) = 0.42
P(L|C) = P(L n C) ÷ P(C)
P(L n C) = P(L|C) × P(C) = 0.04 × 0.42 = 0.0168
P(L|B) = P(L n B) ÷ P(B)
P(L n B) = P(L|B) × P(B) = 0.15 × 0.58 = 0.087
P(L) = P(L n C) + P(L n B) = 0.0168 + 0.087 = 0.1038 (Since the bus and the car are the two only options)
The approximate probability that Kevin chose to get home from work by bus, given that he arrived home after 7 pm
= P(B|L) = P(B n L) ÷ P(L)
P(B n L) = P(L n B) = 0.087
P(L) = 0.1038
P(B|L) = (0.087/0.1038) = 0.838150289 = 0.838
Hope this Helps!!!
