If the skier starts at point A, in how many different ways can the skier reach the point E? If the skier starts at point A, find the probability that the skier will reach the point E. - Junior Cycle Mathematics - Question b - 2013

To find the probability of reaching point E, we first need to identify the total number of possible routes from point A:

1. Routes from A: The skier can go to B (2 ways), C (2 ways), or D (3 ways).

   Therefore, the total number of routes from point A = 2 (to B) + 2 (to C) + 3 (to D) = 7 ways.

2. Successful Routes to E: Out of the total routes, the successful routes to point E are:

   • A → B → E (1 way)
   • A → B → D → E (1 way)
   • A → D → E (1 way)

   Thus, there are 3 successful routes to reach point E.

3. Probability Calculation: The probability can be calculated as: $P(E) = \frac{\text{Number of Successful Routes}}{\text{Total Routes}} = \frac{3}{7}$

So, the probability that the skier will reach point E is ( \frac{3}{7} ).