Financial Risk Manager Part 1

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The probability of an increase in the annual dividend paid out to shareholders of ABC Limited is 0.4. The probability of an increase in share price given an increase in dividends is 0.7. Determine the joint probability of an increase in dividends and an increase in the share price.

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TTanishq

0.28

0.14

0.72

0.3

Explanation:

Explanation

Let:

A be the event that the dividend is increased
B be the event that the share price increases

Given:

P(A) = 0.4 (probability of dividend increase)
P(B | A) = 0.7 (probability of share price increase given dividend increase)

The joint probability of an increase in dividends and an increase in share price is P(B ∩ A).

Using the multiplication rule of probability:

P(B|A) = \frac{P(B \cap A)}{P(A)}

Rearranging the formula:

P(B \cap A) = P(B|A) \times P(A) = 0.7 \times 0.4 = 0.28 \text{ or } 28\%

Note: P(A ∩ B) = P(B ∩ A) since the intersection of events is commutative.

Therefore, the joint probability of both events occurring is 0.28.

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