Of 162 students honored at an academic awards banquet, 48 won awards for mathematics and 78 won awards for English. There are 14 students who won awards for both mathematics and English. A newspaper chooses a student at random for an interview. What is the probability that the student interviewed won an award for English or mathematics?

Needing an explained version or could you plz make this question a little simplier...plz?

Thank You So Much!!

To find the probability that the student interviewed won an award for English or mathematics, we need to calculate the total number of students who won an award for English or mathematics and divide it by the total number of students.

Let's break down the information given:

- A total of 162 students were honored at the academic awards banquet.
- Out of these, 48 students won awards for mathematics.
- 78 students won awards for English.
- There are 14 students who won awards for both mathematics and English.

To find the total number of students who won an award for either English or mathematics, we need to add the number of students who won awards for English and the number of students who won awards for mathematics. However, we must remember to subtract the number of students who won awards in both subjects once to avoid double counting.

So, to calculate the total number of students who won an award for English or mathematics, we can use the formula:

Total = English + Math - Both

Total = 78 + 48 - 14
Total = 112

Therefore, there are 112 students who won an award for either English or mathematics.

Now, to find the probability, we divide the number of students who won an award for English or mathematics by the total number of students:

Probability = (English or Math) / Total

Probability = 112 / 162
Probability ≈ 0.6914

So, the probability that the student interviewed won an award for English or mathematics is approximately 0.6914 or 69.14%.

To solve this problem you need to do as shown below.

P(A or B) = P(A) + P(B) → _Write disjoint probability formula._
= P(A)/(Total#) + P(B)/(Total#)
= 48/162 + 78/162 → _Add._
= 112/162 → _Simplify if possible._
= 0.6914 → _Use a Calculator._

So as you can see ↓
the answer is 112/162 or 0.619

Answering yourself! How weird is that??!!