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A store sells four brands of tablets. The least expensive
Chapter 1, Problem 8E(choose chapter or problem)
PROBLEM 8E
A store sells four brands of tablets. The least expensive brand, B1, accounts for 40% of the sales. The other brands (in order of their price) have the following percentages of sales: B2, 30%; B3, 20%; and B4, 10%. The respective probabilities of needing repair during warranty are 0.10 for B1, 0.05 for B2, 0.03 for B3, and 0.02 for B4. A randomly selected purchaser has a tablet that needs repair under warranty. What are the four conditional probabilities of being brand Bi, i = 1, 2, 3, 4?
Questions & Answers
QUESTION:
PROBLEM 8E
A store sells four brands of tablets. The least expensive brand, B1, accounts for 40% of the sales. The other brands (in order of their price) have the following percentages of sales: B2, 30%; B3, 20%; and B4, 10%. The respective probabilities of needing repair during warranty are 0.10 for B1, 0.05 for B2, 0.03 for B3, and 0.02 for B4. A randomly selected purchaser has a tablet that needs repair under warranty. What are the four conditional probabilities of being brand Bi, i = 1, 2, 3, 4?
ANSWER:
Solution 8E
Step1 of 3:
We have,
Probability that the tablets need repair = P(R)
Probability that the least expensive brands are
P() = 40%
= 0.4
P() = 30%
= 0.3
P() = 20%
= 0.2
P() = 10%
= 0.1
Similarly,
P(R/) = 0.10
P(R/) = 0.05
P(R/) = 0.03
P(R/) = 0.02
We need to find,
What are the four conditional probabilities of being brand Bi, i = 1, 2, 3, 4?
Step2 of 3:
We need to find the Probability that the tablets need repair and it is given by
P(R) = P(R) + P(R
) + P(R
) + P(R
) ………(1)
Where,
1).P(R) = P(
)
P(R/
) [Because P(R/
) =
]
= 0.40.10
= 0.04
Hence, P(R) = 0.04.
2).P(R) = P(
)
P(R/
) [Because P(R/
) =
]
= 0.30.05