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Bruce has just purchased 100 shares of Out Clone,inc. stock. the company is seeking FDA approval for a treatment that relieves the common cold. according to pharmaceutical experts, there is a 50% chance that FDA approval will be granted, and according to market insiders, there is an 85% chance the value of the stock will double if FDA approval is granted. what is the probability that the FDA will approve the treatment and the value of Bruce's investments will double?​

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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