Use the table to calculate the probability that it is a Thursday, given that Jemma has travelled to work either by a train or a bus? The table show the relative frequencies with which Jemma uses each type of transport on her two travel day.
2 Answers
Explanation:
The probability is written as
To fond this probability, we find the probability that either a bus or train was taken and divide it by the probability a bus or train was taken.
Explanation:
Note that
For brevity, let us write:
#{ (T = "Train"), (C = "Car"), (B = "Bus"), ("Mo" = "Monday"), ("Th" = "Thursday") :}#
Then:
#P("Th" | (T uu B)) = (P("Th" nn (T uu B)))/(P(T uu B))#
Now:
#P("Th" nn (T uu B)) = P("Th" nn T) + P("Th" nn B) = 0.18 + 0.17 = 0.35#
and:
#P(T uu B) = P(("Mo" uu "Th") nn (T uu B))#
#color(white)(P(T uu B)) = P(("Mo" nn T) uu ("Mo" nn B) uu ("Th" nn T) uu ("Th" nn B))#
#color(white)(P(T uu B)) = P("Mo" nn T) + P("Mo" nn B) + P("Th" nn T) + P("Th" nn B)#
#color(white)(P(T uu B)) = 0.15+0.20+0.18+0.17 = 0.70#
So:
#P("Th" | (T uu B)) = (P("Th" nn (T uu B)))/(P(T uu B)) = 0.35/0.70 = 0.50#