Question

An investment advisor believes that there is a 60% chance of making money by investing in a specific stock. If the stock makes money, then there is a 50% chance that among those making money, they would also get a dividend. Find the probability that the investor makes money and receive a dividend.

Answer 1

Answer:

$\mathbf{ 0.6 \times 0.5 = 0.3 }$

Step-by-step explanation:

Let M denote the event that the stock makes money and D denote the event that the stock pays dividends.

It is given that $P(M) = 0.6$

Observe that the two events M and D are not independent because if the stock doesn't make money then it will not pay dividends. Therefore the event $D | M^{c}$ (D given M does not occur) is a null event, i.e

$P(D|M^{c}) = 0$

It is also given that,

$P(D|M) = 0.5$

Recall that : $P(D|M) = \frac{P(D \cap M)}{P(M)}$

Here, we are required to find $P(D \cap M)$

$P(D \cap M) =P(D|M) \times P(M)= 0.5 \times 0.6 = 0.3$