Answer :
Answer:
5% probability neither truck is available
Step-by-step explanation:
We solve this problem building the Venn's diagram of these probabilities.
I am going to say that:
A is the probability that the first truck is available.
B is the probability that the second truck is available.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that the first truck is available and the second one is not [tex]A \cap B[/tex] is the probability that both trucks are available.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
The probability that both trucks are available is .30.
This means that [tex]A \cap B = 0.3[/tex]
The probability the second truck is available is .50
This means that [tex]B = 0.5[/tex]. So
[tex]B = b + (A \cap B)[/tex]
[tex]0.5 = b + 0.3[/tex]
[tex]b = 0.2[/tex]
The probability the first truck is available is .75
This means that [tex]A = 0.75[/tex]. So
[tex]A = a + (A \cap B)[/tex]
[tex]0.75 = a + 0.3[/tex]
[tex]a = 0.45[/tex]
The probability that at least one truck is available is:
[tex]A \cup B = a + b + (A \cap B) = 0.45 + 0.2 + 0.3 = 0.95[/tex]
The probability that neither truck is available is:
[tex]1 - (A \cup B) = 1 - 0.95 = 0.05[/tex]
5% probability neither truck is available
