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

Engineering

Mathematics

Conditional Probability

Question

$\frac{4}{12}$

$\frac{5}{12}$

$\frac{7}{12}$

none of these

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Let A denote the event 'stock price will go up', and B be the event 'stock price will remain same'.

Then $P (A) = \frac{1}{3}$ and $P (B) = \frac{1}{4}$
∴ P(stock price will either go up or remain same) is

$P (A \cup B) = P (A) + P (B) = \frac{1}{3} + \frac{1}{4} = \frac{7}{12}$
Hence probability that stock price will go down is given by

$P (A \cap B) = 1 - P (A \cup B) = 1 - \frac{7}{12} = \frac{5}{12}$

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