Suppose that 34% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 30% end up investing in bonds, and 35% end up investing in stocks or bonds (or both). What is the probability that a person who inquires about investments at this firm will invest in both stocks and bonds?
I get this but i can't remember what else I do
The "AND" are is shared. This is the key.
Abandoning the lengthy names:
A + S = 0.34 ==> S = 0.34 - A
A + B = 0.30 ==> B = 0.30 - A
S + B - A = 0.35
Suppose that % of the people who inquire about investments at a certain brokerage firm end up investing in stocks, % end up investing in bonds, and % end up investing in stocks or bonds (or both). What is the probability that a person who inquires about investments at this firm will invest in both stocks and bonds?
To find the probability that a person will invest in both stocks and bonds, we can use the concept of set theory and the inclusion-exclusion principle.
Let's define two events:
Event A: a person will invest in stocks
Event B: a person will invest in bonds
We are given the following probabilities:
P(A) = 34% = 0.34
P(B) = 30% = 0.30
P(A ∪ B) = 35% = 0.35
To find the probability of a person investing in both stocks and bonds (A ∩ B), we can use the inclusion-exclusion principle:
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Substituting the given values, we get:
P(A ∩ B) = 0.34 + 0.30 - 0.35
Simplifying this equation gives:
P(A ∩ B) = 0.29
Therefore, the probability that a person who inquires about investments at this firm will invest in both stocks and bonds is 0.29 or 29%.