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 need to start by representing the two coaches (Ahmed and Usman) as the first level of branches.
Under each coach, we will represent the probability of being a goalkeeper or not being a goalkeeper.
So, the probability tree diagram would look like this:
Ahmed (0.6)
/ \
Goalkeeper (0.5) Not a Goalkeeper (0.5)
Usman (0.4)
/ \
Goalkeeper (0.3) Not a Goalkeeper (0.7)
b) To find the probability of being a goalkeeper today, we need to consider the probabilities of being a goalkeeper under each coach and the probabilities of each coach being chosen.
The probability of being a goalkeeper today can be calculated using the following formula:
Probability = (Probability of choosing Ahmed) x (Probability of being a goalkeeper under Ahmed) + (Probability of choosing Usman) x (Probability of being a goalkeeper under Usman)
Probability = (0.6) x (0.5) + (0.4) x (0.3)
Probability = 0.3 + 0.12
Probability = 0.42
Therefore, the probability that you will be a goalkeeper today is 0.42 or 42%.