The probability that Don's car passes the MOT test next time is 4/5, that Mag's car passes is 5/7 and that Joe's car passes is 1/2.
Find the probability that a)all three will pass b)just two out of the three will pass c)no car passes?
(might need a probability tree)
PLEASE HELP!
(a) (4/5)x(5/7)x(1/2)= ?
(b) Add the probabilities that only Don, only Mag and only Joe pass
(1/5)(5/7)(1/2) + (4/5)(2/7)(1/2) + (4/5)(5/7)(1/2) = ?
(c) (1/5)x(2/7)x(1/2)+ ?
To find the probabilities in this scenario, we can use a probability tree. Here is how you can construct and use it to find the required probabilities:
Step 1: Draw the probability tree
Start by drawing a vertical line and label it with the three names: Don, Mag, and Joe. At each branch, write the probability of passing or failing the MOT test.
```
|
Don
/ | \
/ | \
/ | \
4/5 1/5
/ \
| |
Mag Joe
\ /
\ /
\ /
5/7 2/7
```
Step 2: Calculate the probabilities
a) To find the probability that all three cars pass, multiply the probabilities along the branch that leads to Don, then to Mag, and finally to Joe: (4/5) * (5/7) * (1/2) = 20/70 = 2/7.
b) To find the probability that exactly two out of the three cars pass, we need to consider all possible combinations. There are three scenarios to consider: Don and Mag pass while Joe fails, Don and Joe pass while Mag fails, and Mag and Joe pass while Don fails.
Scenario 1: Don and Mag pass, Joe fails: (4/5) * (5/7) * (1/2) = 2/7
Scenario 2: Don and Joe pass, Mag fails: (4/5) * (2/7) * (1/2) = 4/35
Scenario 3: Mag and Joe pass, Don fails: (1/5) * (5/7) * (1/2) = 5/70 = 1/14
Now, add the probabilities from all three scenarios: 2/7 + 4/35 + 1/14 = 38/70 = 19/35.
c) To find the probability that no car passes, multiply the probabilities along the branches where each car fails: (1/5) * (2/7) * (1/2) = 2/70 = 1/35.
Step 3: Interpret the results
a) The probability that all three cars pass the MOT test is 2/7.
b) The probability that exactly two out of the three cars pass is 19/35.
c) The probability that no car passes is 1/35.
Remember, probability trees are useful for visualizing and calculating probabilities in scenarios with multiple events. They help break down complex problems and make calculations easier.