# Thread: probability with tree diagram

1. ## probability with tree diagram

Hi, this is my question:

Sanjit enters a competition where he takes part in two events.
The probability that he will win the running event is 0.3.
The probability that he will win the cycling event is 0.6.
The two events are independant.

A) calculate the probability that Sanjit will win both events.

when drawing a tree diagram for this question would i do this?

and to get the answer would i do 0.3 x 0.6= 0.18?

Thanks!

The first step of the tree diagram is one of the races (outcome: win or lose), the second step of the tree diagram is the other race (outcome: win or lose)

3. Originally Posted by SpringFan25

The first step of the tree diagram is one of the races (outcome: win or lose), the second step of the tree diagram is the other race (outcome: win or lose)

so i don't need to put 0.5 on the R and the C, all i put is what race it is?

4. yes

5. also the next parts says:
B) Calculate the probability that Sanjit will win exactly one of the two events?

for this question woould it be 1/4?

6. There are 2 ways this event can happen:

Win then lose. Probability = (0.3 * 0.4)
Lose then Win. Probability = (0.7 * 0.6)

Total probability = (0.3*0.4)+(0.7*0.6) = 0.54

To get the probabilities for each outcome, just follow the relevant path on the the tree, multiplying together the probability values of each branch you walk along.