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Sagot :
To determine the probability that the FDA will approve the treatment and the value of Bruce's investments will double, we need to consider the following probabilities:
1. The probability that the FDA will grant approval for the treatment, \( P(A) \), is 50% or 0.50.
2. The probability that the value of the stock will double given that FDA approval is granted, \( P(B|A) \), is 85% or 0.85.
We are looking for the joint probability that both events will occur: FDA approval is granted and the stock value will double. This is represented as \( P(A \cap B) \).
The joint probability of two events \( A \) and \( B \) occurring is given by:
\[ P(A \cap B) = P(A) \times P(B|A) \]
Substituting the given probabilities:
\[ P(A \cap B) = 0.50 \times 0.85 = 0.425 \]
Therefore, the probability that the FDA will approve the treatment and the value of Bruce's investments will double is 0.425, or 42.5%.
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