To find the probability that a randomly selected student is either female or right-handed, we will use the principle of addition in probability.

Let:

• $P(\text{Female})$ be the probability of selecting a female.
• $P(\text{Right-handed})$ be the probability of selecting a right-handed student.
• $P(\text{Female and Right-handed})$ be the probability of selecting a student who is both female and right-handed.

The formula for the probability of $A$ or $B$ is: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Step 1: Find $P(\text{Female})$

The number of females is 53 out of 119 total students, so: $P(\text{Female}) = \frac{53}{119}$

Step 2: Find $P(\text{Right-handed})$

The number of right-handed students is 90 out of 119 total students, so: $P(\text{Right-handed}) = \frac{90}{119}$

Step 3: Find $P(\text{Female and Right-handed})$

The number of students who are both female and right-handed is 41, so: $P(\text{Female and Right-handed}) = \frac{41}{119}$

Step 4: Calculate $P(\text{Female or Right-handed})$

Now, we can apply the addition rule: $P(\text{Female or Right-handed}) = P(\text{Female}) + P(\text{Right-handed}) - P(\text{Female and Right-handed})$ Substitute the values: $P(\text{Female or Right-handed}) = \frac{53}{119} + \frac{90}{119} - \frac{41}{119}$ Simplifying the expression: $P(\text{Female or Right-handed}) = \frac{53 + 90 - 41}{119} = \frac{102}{119}$

Thus, the probability that a randomly selected student is either female or right-handed is: $\boxed{\frac{102}{119}} \approx 0.857$

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. What is the probability that a student is male or left-handed?
2. What is the probability that a student is both male and left-handed?
3. If two students are randomly selected, what is the probability that both are female?
4. What is the probability that a student is not right-handed?
5. What is the probability that a randomly selected student is both female and left-handed?

Tip: The principle of addition in probability helps avoid double-counting overlapping outcomes.