Answer:
The probability is 0.64
Step-by-step explanation:
What we want to calculate here is conditional probability.
Let P(A )= Probability of using route A = 50% = 0.5
Let P( B )= probability of using route B = 25% = 0.25
Let P (C )= probability of using route C = 25% = 0.25
Let T be the probability that he will be in a traffic Jam
The probability that he will be in a traffic Jam if he uses route A = 80%
Mathematically this is written as P( T | A) which is read as probability of T given A
so P( T | A) = 0.8
Same way for B and C which can be written as follows;
P( T | B) = 60% = 0.6
P( T | C) = 30% = 0.3
Now, what do we want to calculate?
He is in a traffic Jam, and we want to find the probability that he used route A. This means we want to find P(A) given T which can be written mathematically as P ( A | T)
We can find this using the other parameters and especially the equation below;
P ( A | T) = P(A) • P( T| A) / {P(A) • P ( T | A) + P(B)• P(T| B) + P(C) • P(T|C)
P( A | T) = (0.5 * 0.8)/ ( 0.5)(0.8) + (0.25)(0.6) + (0.25)(3) = 0.4/(0.4 + 0.75 + 0.075) = 0.4/0.625 = 0.64
