Question

question 3
3 pts
explain the process of finding the probability of the following. you will earn points for the explanation!
of the 200 students in the junior class, 78 of them are in algebra, 85 of them are in geometry and 14 are in both. what is the probability that a junior is in algebra or geometry? explain!
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12pt paragraph b i u a t² :

Explanation:

Step1: Use the formula for P(A or B)

The formula for the probability of event A or event B is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, let event A be being in Algebra and event B be being in Geometry. The total number of students $n = 200$.

Step2: Calculate P(A), P(B) and P(A ∩ B)

$P(A)=\frac{78}{200}$, $P(B)=\frac{85}{200}$ and $P(A\cap B)=\frac{14}{200}$.

Step3: Substitute values into the formula

$P(A\cup B)=\frac{78}{200}+\frac{85}{200}-\frac{14}{200}=\frac{78 + 85- 14}{200}=\frac{149}{200}=0.745$.

Answer:

The probability that a Junior is in Algebra or Geometry is $\frac{149}{200}$ or $0.745$.