Question 1201093: According to the store’s historical records, 65% of its digital camera customers
are male, 18% of its digital camera customers purchased the extended warranty,
and 10% of its digital camera customers are female and purchased the extended
warranty.
(i) Determine the probability that a male digital camera customer will
purchase the extended warranty. [4 Marks]
(ii) Are female customers more likely to purchase the extended warranty?
Justify your answers
Answer by GingerAle(43)   (Show Source):
You can put this solution on YOUR website! Certainly, let's analyze the probabilities related to digital camera customers and extended warranties.
**i) Probability of a male customer purchasing the extended warranty**
* **Let's define the events:**
* M: Event that a customer is male
* F: Event that a customer is female
* W: Event that a customer purchases the extended warranty
* **Given probabilities:**
* P(M) = 0.65 (Probability of a male customer)
* P(W) = 0.18 (Probability of purchasing the extended warranty)
* P(F ∩ W) = 0.10 (Probability of a female customer purchasing the extended warranty)
* **Find P(M ∩ W) (Probability of a male customer purchasing the extended warranty):**
* We know:
* P(M ∪ F) = 1 (Since all customers are either male or female)
* P(W) = P(M ∩ W) + P(F ∩ W)
* Therefore:
* P(M ∩ W) = P(W) - P(F ∩ W)
* P(M ∩ W) = 0.18 - 0.10 = 0.08
* **Calculate the conditional probability P(W | M):**
* P(W | M) = P(M ∩ W) / P(M) = 0.08 / 0.65 ≈ 0.1231
**Therefore, the probability that a male digital camera customer will purchase the extended warranty is approximately 0.1231 or 12.31%.**
**ii) Are female customers more likely to purchase the extended warranty?**
* **Find the probability of a female customer purchasing the extended warranty:**
* P(W | F) = P(F ∩ W) / P(F)
* P(F) = 1 - P(M) = 1 - 0.65 = 0.35
* P(W | F) = 0.10 / 0.35 ≈ 0.2857
* **Compare the probabilities:**
* P(W | M) ≈ 0.1231
* P(W | F) ≈ 0.2857
* **Conclusion:**
* Since P(W | F) > P(W | M), **female customers are more likely to purchase the extended warranty.**
I hope this helps! Let me know if you have any other questions.
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