Answer:
The probability that it rained that morning, given that the plane was late P( R | L) = 70%
Step-by-step explanation:
We shall be using Baye’s theorem to solve this;
Let the event that it rains be R
Let the event that it does not rain be N
Let the event that the plane is late be L
From the question;
P( R) that morning = 40% = 0.4
P(N) that morning = 60% = 0.6
P(L | R) read as probability that the plane is late , given that it rained = 70% = 0.7
P( L | N) read as probability that the plane is late given that there is no rain = 20% = 0.2
Now, we want to calculate P ( R | L) which is read as probability that it rained given that the plane was late
What we shall use to solve this issue is the Baye’s theorem of conditional probability.
By Baye’s theorem;
P( R | L) ={ P(L | R) * P(R) }/( P( R) * P (L | R) + P(N) * P(L | N)
Substituting the values;
P(R | L) = (0.7 * 0.4)/(0.4 * 0.7) + (0.6 * 0.2)
P(R | L) = 0.28/(0.28 + 0.12)
P( R | L) = 0.28/0.4
P( R | L) = 0.7 = 70%
