Find the missing probability.

P(A)=7/20,P(A∩B)=49/400,P(B)=?                                                                                                                 A. 15
B. 720
C. 710
D. 310

To solve for \( P(B) \), we use the following relationship between the probabilities of events A and B:

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

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

We need to find \( P(B) \). The formula can be rearranged to solve for \( P(B) \):

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

Substitute the given values:

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

Convert the division into multiplication by the reciprocal:

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

Simplify the expression:

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

\[ P(B) = \frac{980}{2800} \]

\[ P(B) = \frac{49}{140} \]

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

Convert the fraction to a decimal:

\[ P(B) = 0.35 \]

None of the provided answer choices directly correspond to the probability, as they appear to be numbers without units. Ensure the choices match the context:

\[ \text{A. 15} \]
\[ \text{B. 720} \]
\[ \text{C. 710} \]
\[ \text{D. 310} \]

Given these choices, none represent the calculated probability directly. However, the answer choice seems not relevant to probability values.

Please review the context or provided options, and if they are consistent with the expected result, which should be the decimal equivalent of the probability.

Do you have any questions or need further details?

Here are 5 more questions you might want to ask:
1. How do you find the probability of the union of two events?
2. Can you explain Bayes' Theorem?
3. What is the difference between independent and dependent events?
4. How do you calculate the expected value of a random variable?
5. Can you demonstrate the use of the Law of Total Probability?

**Tip:** When calculating probabilities, always double-check to ensure that the final answer falls within the range of 0 to 1, as probabilities cannot exceed this range.

Learn how to calculate the missing probability P(B) given P(A) = 7/20 and P(A ∩ B) = 49/400 using set theory and probability formulas. This problem involves understanding the relationship between events A and B in a probabilistic context. Suitable for high school students learning probability concepts.

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