Answer:
a. 5%
b. 55%
c. 70%
Step-by-step explanation:
a. The probability of customer wanting both services (P(O&T)) is:
[tex]P(O)+P(T)+P(O\&T) = 0.75\\P(O)+P(O\&T) =0.60\\P(T)+P(O\&T) = 0.20\\P(O)+P(T)+P(O\&T) -[P(O)+P(T)+2P(O\&T)]=0.75 -(0.60-0.20)\\P(O\&T)=0.05=5\%[/tex]
The probability is 5%
b. The probability that the customer will need an oil change, but not a tire rotation (P(O)) is :
[tex]P(O)+P(O\&T) = 0.60\\P(O\&T) = 0.05\\P(O) =0.60-0.05 = 0.55 = 55\%[/tex]
The probability is 55%
c. The probability that the customer will want exactly one of these two services (P(O)+P(T)) is:
[tex]P(O)+P(T)+P(O\&T) = 0.75\\P(O\&T) = 0.05\\P(O)+P(T) =0.75-0.05 = 0.70 = 70\%[/tex]
The probability is 70%
Answer:
a) P(C∩T) = 0.05
b) P(C) = 0.55
c) P(C) + P(T) = 0.70
Step-by-step explanation:
Given:
60% of the customers require an oil change
20% require tire rotation
75% of customers require at least one of these services.
So,
Let C represent customers that requires oil change and
T represent customers that requires tire rotation.
P(C) + P(C∩T) = 60% = 0.6 .......1
P(T) + P(C∩T) = 20% = 0.2. .......2
P(C) + P(T) + P(C∩T) = 75% = 0.75 .....3
a) the probability that the customer needs both services P(C∩T).
From eqn 1 , 2 , 3 above.
P(C∩T) = eqn 1 + eqn 2 - eqn 3
P(C∩T) = 0.60 + 0.20 - 0.75
P(C∩T) = 0.05 or 5%
b) from eqn 1:
P(C) = 0.60 - P(C∩T)
P(C) = 0.60 - 0.05
P(C) = 0.55 or 55%
c) the probability that a customer will want exactly one of the two services P(C) + P(T).
Adding eqn 1 and 2 we have;
P(C) + P(T) + 2 P(C∩T) = 0.60 +0.20
P(C) + P(T) = 0.80 - 2P(C∩T)
P(C) + P(T) = 0.80 -2(0.05) = 0.70 or 70%
