"quantity"exercise: joint probability

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Questions 1:

Event X and Event Y are independent events. The probability of X is 0.2 [P(X) = 0.2] and the probability of Y is 0.5 [P(Y) = 0.5]. The joint probability of X and Y, P(XY), is closest to:

A、 0.7.

B、 0.3.

C、 0.1.

Questions 2:

An investor in Abco stock forecasts the probability that Abco exceeded, met, or fell short of consensus expectations for free cash flow (FCF) during the prior

quarter:

● P(FCF exceeded consensus) = 0.50

● P(FCF met consensus) = 0.35

● P(FCF fell short of consensus) = 0.15

While waiting for Abco to release last quarter’s FCF data, the investor learns that Abco will acquire a competitor. Believing that the upcoming acquisition makes it more likely that last quarter’s FCF will exceed the consensus, the investor generates a list of FCF events that may have influenced the acquisition:

● P(Acquisition | FCF exceeded consensus) = 0.40

● P(Acquisition | FCF met consensus) = 0.25

● P(Acquisition | FCF fell short of consensus) = 0.35

Using Bayes’ Formula, calculate the probability that Abco is likely to exceed consensus FCF expectations for last quarter given the acquisition. P(FCF exceeded consensus | Acquisition) is closest to:

A、 34%.

B、 59%.

C、 27%.

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