Question

An investment consultant predicts that the odds against the price of a certain stock will go up during the next week are $2:1$ and the odds in favor of the price remaining the same are $1:3$. The probability that the price of the stock will go down during the next week, is

• A. $\frac{4}{12}$
• B. $\frac{5}{12}$
• C. $\frac{7}{12}$
• D. none of these

Answer 1

The correct option is B $\frac{5}{12}$

Let $A$ denote the event 'stock price will go up', and $B$ be the event 'stock price will remain same'.
Then $P\left(A\right)=\frac{1}{3}$ and $P\left(B\right)=\frac{1}{4}$.
$\therefore P($ stock price will either go up or remain same $)$ is
$P(A\cup B)=P\left(A\right)+P\left(B\right)=\frac{1}{3}+\frac{1}{4}=\frac{7}{12}$
Hence probability that stock price will go down is given by
$P(\overline{A}\cap \overline{B})=1-P(A\cup B)=1-\frac{7}{12}=\frac{5}{12}$