Question

A survey was taken of 1,000 people's investment choices. The survey indicates that 34% have invested in stocks (S), 48% have invested in bonds (B), and 21% have invested in stocks and bonds.

1. If someone invested in bonds, what is the probability that the person did not invest in stocks? Write a probability statement and round to three decimals.
2. Find the odds against the event in part "a". Be sure to write the odds in most reduced form.

Thank you!

Answer 1

P(S) = 0.34

P(B) = 0.48

P(S∩B) = 0.21

We want to find, If someone invested in bonds, what is the probability that the person did not invest in stocks.

That is P(S'∩B) where S' is compliment of event S

P(S'∩B) = P(B) - P(S∩B)

= 0.48 - 0.21

= 0.27

Odds against the event S'∩B is defined as P[(S'∩B)'] / P(S'∩B)

That is ratio of the probability that the event will not occur to the probability that the event will occur

odds against = (1-0.27)/0.27

= 0.73/0.27

= 2.704