Consider randomly selecting buyer and memory card purchased

Solved Step by Step With Explanation- Dependent Events Analysis

Questions

(d) Are the events A and B independent ? Justify it.

Answers

40% of buyers include an extra battery (B) in their purchase.

30% of buyers include both a memory card and an extra battery.

P(B) = 0.40 (battery purchased)

The probability of the union of A and B (P(A ∪ B)) can be calculated using the inclusion-exclusion principle:

We want to find the conditional probability of an optional card being purchased (A) given that an extra battery was purchased (B). This can be calculated using the formula for conditional probability:

P(A | B) = P(A ∩ B) / P(B)

Here, we're interested in the probability of an extra battery being purchased (B) given that an optional memory card was purchased (A). This can be calculated similarly using the conditional probability formula:

P(B | A) = P(A ∩ B) / P(A)

Two events, A (memory card purchased) and B (battery purchased), are considered independent if the occurrence of one event does not affect the probability of the other event occurring. Mathematically, for independent events:

P(A | B) = P(A) and P(B | A) = P(B)

The given scenario involves probabilities of purchasing an optional memory card and an extra battery with a certain digital camera. We calculated the probabilities of these events, explored their conditional probabilities, and determined that the events are dependent. This dependency arises due to the fact that the probability of one event changes based on the occurrence of the other event, indicating a connection between the two purchase decisions.