Question

alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price fhat fund A rises in price. There is also a 20% chance that fund b will rise in price. What is the probablity that at least one of the funds will rise in price?

Answer 1

0.36

Explanation:

We are given that Alison has all her money invested in two mutual funds A and B.

Probability that A will rise=
`P(A)=0.40`

Probability that B rises given that A rise =
`P(B/A)=0.60`

Probability that B will rise
`P( B)=0.20`

We have to find the probability that atleast one of the funds will rise in price.

`P(B/A)=(P(A\cap B))/(P(A))`

Substitute the values then we get

`0.60=(P(A\cap B))/(0.40)`

`P(A\cap B)=0.60* 0.40=0.24`

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

`P(A\cup B)=0.40+0.20-0.24=0.36`

Hence, the probability that atleast one of the funds will rise in price=0.36

Answer 2

0.36

Explanation:

Probability that A will rise: P(A) = 0.4

Probability that B rises given that A rise: P(A|B) = 0.6

Probability B will rise: P(B) = 0.2

Now,

P(A and B) = P(A) * P(A|B) = 0.4 * 0.6 = 0.24

Probability that at least one fund will rise:

P(A or B) = P(A) + P(B) - P(A and B) = 0.4 + 0.2 - 0.24 = 0.36

So,

Probability that at least one of the funds will rise in price = 0.36