Answer :
Answer:
[tex]\mathbf{ 0.6 \times 0.5 = 0.3 }[/tex]
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 [tex] P(M) = 0.6 [/tex]
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 [tex] D | M^{c} [/tex] (D given M does not occur) is a null event, i.e
[tex] P(D|M^{c}) = 0[/tex]
It is also given that,
[tex] P(D|M) = 0.5 [/tex]
Recall that : [tex] P(D|M) = \frac{P(D \cap M)}{P(M)} [/tex]
Here, we are required to find [tex] P(D \cap M) [/tex]
[tex]P(D \cap M) =P(D|M) \times P(M)= 0.5 \times 0.6 = 0.3[/tex]