At a certain gas station, 45% of the customers use regular unleaded gas, 30% use extra unleaded gas and 25% use premium unleaded gas. Of those customers using regular gas, only 35% fill their tanks. Of those customers using extra gas, 60% fill their tanks, whereas those using premium, 45% fill their tanks.
i) Draw a tree diagram to describe the above situation
ii) What is the probability that the next customer will request premium unleaded gas and will not fill the tank?
iii) What is the probability that the next customer fill the tank?
iv) Given that the next customer fills the tank. What is the probability that extra gas is requested?
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Step-by-step explanation:
Step 1
Probabilities of customers using regular gas:
P
(
A
1
)
=
40
%
=
0.4
Probabilities of customers using plus gas
P
(
A
2
)
=
35
%
=
0.35
Probabilities of customers using premium gas
P
(
A
3
)
=
25
%
=
0.25
We are also given with conditional probabilities of full gas tank:
P
(
B
|
A
1
)
=
30
%
=
0.3
P
(
B
|
A
2
)
=
60
%
=
0.6
P
(
B
|
A
3
)
=
50
%
=
0.5
Step 2: (a)
The probability that next customer will requires plus gas and fill the tank is:
P
(
A
2
∩
B
)
=
P
(
A
2
)
×
P
(
B
|
A
2
)
=
0.35
×
0.60
=
0.21
Therefore,
P
(
A
2
∩
B
)
=
0.21
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