Find the missing probability.

P(A) = 7/20, P(A∩B) = 49/400, P(B) = ?                                                                                                    A. 121/200
B. 7/20
C. 4/5
D. 39/100

To find the missing probability \( P(B) \), we can use the formula for the intersection of two events:

\[ P(A \cap B) = P(A) \cdot P(B | A) \]

However, we can also use the formula for the joint probability:

\[ P(A \cap B) = P(A) \cdot P(B) \]

Given:
\[ P(A) = \frac{7}{20} \]
\[ P(A \cap B) = \frac{49}{400} \]

We need to find \( P(B) \). Rearrange the joint probability formula to solve for \( P(B) \):

\[ P(B) = \frac{P(A \cap B)}{P(A)} \]

Substitute the given values:

\[ P(B) = \frac{\frac{49}{400}}{\frac{7}{20}} \]

To divide fractions, multiply by the reciprocal:

\[ P(B) = \frac{49}{400} \times \frac{20}{7} \]

Simplify the multiplication:

\[ P(B) = \frac{49 \times 20}{400 \times 7} = \frac{980}{2800} = \frac{49}{140} = \frac{7}{20} \]

Therefore, the missing probability \( P(B) \) is:

\[ \boxed{\frac{7}{20}} \]

The correct answer is:

\[ \boxed{B. \frac{7}{20}} \]

Would you like more details or have any questions?

Here are 5 questions you might want to ask:
1. How can I verify the results of a probability calculation?
2. What are the properties of joint probability?
3. How do conditional probabilities relate to joint probabilities?
4. Can you explain the difference between independent and dependent events?
5. How do I interpret the results of probability problems in real-life scenarios?

**Tip:** Always remember to check if the events are independent or dependent, as this can affect how you calculate joint and conditional probabilities.

Learn how to find the missing probability P(B) given P(A) using joint probability formulas. This problem involves calculating probabilities using given values for events A and B. Suitable for students studying probability and statistics in Grades 10-12.

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