0

$A$ always goes to work by a bus or a taxi. If he goes to work by a bus one day, the probability he goes to work by a taxi the next day is $0.4$. If he goes to work by a taxi one day, the probability he goes to work by a bus the next day is $0.7$.

Given that $A$ takes a bus to work on Monday, find the probability that he takes a taxi to work on Wednesday.

Community
  • 1
Anthony
  • 363
  • What's the tricky bit? What have you tried? – an4s Jan 16 '20 at 16:51
  • I'm very dumb so sorry I have tried but still couldn't solve it, the answer is .36 please show me how it was derived, thanks. – Anthony Jan 16 '20 at 16:54
  • As a start, you could draw a probability tree for three days (i.e., Monday, Tuesday, Wednesday). – an4s Jan 16 '20 at 16:55

1 Answers1

1

Hint:

The probability tree for the given problem is illustrated below (I leave the filling of the probabilities as an exercise for the OP):

enter image description here

Consider the following two cases:

  1. $A$ takes the bus on Monday $\rightarrow$ $A$ takes the bus on Tuesday $\rightarrow$ $A$ takes the taxi on Wednesday
  2. $A$ takes the bus on Monday $\rightarrow$ $A$ takes the taxi on Tuesday $\rightarrow$ $A$ takes the taxi on Wednesday

The probabilities of interest are then $\mathbb P\left(B\cap B\cap T\right)$ and $\mathbb P\left(B\cap T\cap T\right)$.

an4s
  • 3,716
  • Yeah I solved it with the hint before the illustration, the Monday to Wednesday was the clue all along where two days have past, I was too transfixed on finding the probability of monday that I didn't quite grasp it, thanks. – Anthony Jan 16 '20 at 17:56