You are off to soccer and love being a goalkeeper, but that depends who is the coach today :
- with coach Ahmed the probablity of being a goalkeeper is 0.5
-with coach Usman the probability of being a goalkeeper is 0.3
Ahmed is coach more often.About 6 out of every 10 games ( a probability of 0.6)
a) Draw a probablity tree diagram to show all the outcomes of the experiment
b) what is the probablity that you will be a goalkeeper today
a) To draw a probability tree diagram, we start by representing the two coaches as separate branches.
First, let's draw the branch for Coach Ahmed:
Ahmed (0.6)
/ \
Goalkeeper (0.5) Not Goalkeeper (0.5)
Next, let's draw the branch for Coach Usman:
Usman (0.4)
/ \
Goalkeeper (0.3) Not Goalkeeper (0.7)
The probability of Coach Ahmed being the coach is 0.6, so we assign that probability to the branch leading to Coach Ahmed. Similarly, the probability of Coach Usman being the coach is 0.4, so we assign that probability to the branch leading to Coach Usman.
Then, within each branch, we assign the probabilities of being a goalkeeper or not being a goalkeeper according to the given probabilities.
b) To find the probability of being a goalkeeper today, we need to consider the probability of each outcome and their respective coaches.
The probability of being a goalkeeper with Coach Ahmed is 0.5, and since he coaches 6 out of every 10 games (probability of 0.6), we multiply these probabilities together:
Probability of being a goalkeeper with Coach Ahmed = 0.6 * 0.5 = 0.3
The probability of being a goalkeeper with Coach Usman is 0.3, and since he coaches 4 out of every 10 games (probability of 0.4), we multiply these probabilities together:
Probability of being a goalkeeper with Coach Usman = 0.4 * 0.3 = 0.12
Since there are only two possibilities (being a goalkeeper with Coach Ahmed or with Coach Usman), we can add these probabilities together:
Final Probability of being a goalkeeper today = Probability of being a goalkeeper with Coach Ahmed + Probability of being a goalkeeper with Coach Usman
= 0.3 + 0.12
= 0.42
Therefore, the probability of being a goalkeeper today is 0.42 or 42%.