Makakuha ng mga sagot sa iyong mga pinakamahahalagang tanong sa IDNStudy.com. Tuklasin ang malalim na sagot sa iyong mga tanong mula sa aming komunidad ng mga bihasang propesyonal.

Given that P(A)=.55, P(B)=.35, and P(A|B)=.85, find p(A and B).


Sagot :

Answer:

To find \( P(A \text{ and } B) \), we use the definition of conditional probability, which is given by:

\[ P(A|B) = \frac{P(A \text{ and } B)}{P(B)} \]

Given:

- \( P(A|B) = 0.85 \)

- \( P(B) = 0.35 \)

Rearranging the formula to solve for \( P(A \text{ and } B) \):

\[ P(A \text{ and } B) = P(A|B) \times P(B) \]

Substitute the given values:

\[ P(A \text{ and } B) = 0.85 \times 0.35 \]

Calculate the result:

\[ P(A \text{ and } B) = 0.2975 \]

So, \( P(A \text{ and } B) = 0.2975 \).