
Antita has a 35% chance of recieving a grade 5 in math and a 60% chance of recieving a grade 5 in physics. She also has a 80% chance of recieving a grade 5 in math or physics. 1) what are the odds that she does not receive an 5 in either statistics or physics. 2) receives a 5 in both statistics and physics.

We can solve the problem using probability rules. Let's define:

- \( P(M) \) as the probability that Antita receives a grade 5 in Math, which is \( 35\% = 0.35 \).
- \( P(P) \) as the probability that Antita receives a grade 5 in Physics, which is \( 60\% = 0.60 \).
- \( P(M \cup P) \) as the probability that Antita receives a grade 5 in either Math or Physics, which is \( 80\% = 0.80 \).

### 1. Probability that Antita does **not** receive a 5 in **either** Math or Physics

We need to calculate the complement of the event that Antita receives a grade 5 in either Math or Physics. The probability of **not** receiving a grade 5 in either subject is given by the complement of \( P(M \cup P) \):

\[
P(\text{not } (M \cup P)) = 1 - P(M \cup P)
\]

Substituting the value:

\[
P(\text{not } (M \cup P)) = 1 - 0.80 = 0.20
\]

So, the probability that she does not receive a 5 in either Math or Physics is \( 0.20 \) or 20%.

### 2. Probability that Antita receives a 5 in **both** Math and Physics

We can use the formula for the union of two events to find \( P(M \cap P) \), the probability that she receives a grade 5 in both subjects:

\[
P(M \cup P) = P(M) + P(P) - P(M \cap P)
\]

Rearranging the formula to solve for \( P(M \cap P) \):

\[
P(M \cap P) = P(M) + P(P) - P(M \cup P)
\]

Substituting the values:

\[
P(M \cap P) = 0.35 + 0.60 - 0.80 = 0.15
\]

So, the probability that Antita receives a 5 in both Math and Physics is \( 0.15 \) or 15%.

### Final Answers:
1. The probability that she does not receive a 5 in either Math or Physics is **20%**.
2. The probability that she receives a 5 in both Math and Physics is **15%**.

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Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:
1. What is the probability that Antita receives a 5 in Math but not in Physics?
2. What is the probability that she receives a 5 in Physics but not in Math?
3. How would these probabilities change if the chance of getting a 5 in Physics were reduced to 50%?
4. What is the complement of receiving a grade 5 in both Math and Physics?
5. How do we compute conditional probabilities in this context?

**Tip:** In probability problems, understanding when to apply the complement rule can simplify many calculations!

Antita has a 35% chance of receiving a grade 5 in math and a 60% chance of receiving a grade 5 in physics. She also has an 80% chance of receiving a grade 5 in math or physics. 1) What are the odds that she does not receive a 5 in either math or physics? 2) What are the odds that she receives a 5 in both math and physics?

Solve a probability problem where Antita has a 35% chance of getting a grade 5 in math and 60% in physics. Learn how to calculate the probability that she does not receive a 5 in either subject and the probability that she receives a 5 in both. Suitable for Grades 9-12.

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