Question

a school has 200 students. 120 play sports and 80 dont play sports. of those who play sports, 90 are passing all classes. of those who dont play sports, 60 are passing all classes. if you randomly select a student who is passing all classes, what is the probability they play sports?
90/120 = 0.75
120/200 = 0.60
90/150 = 0.60
90/200 = 0.45
two dice are rolled. event a is first die shows 4 and event b issum of both dice is 8. to determine if these events are independent, you need to check if p(a|b) = p(a). what is p(a|b)?
1/36
1/5
4/36
1/6

Explanation:

Step1: Calculate total number of students passing all classes

The number of students passing all classes who play sports is 90, and the number of students passing all classes who don't play sports is 60. So the total number of students passing all classes is $90 + 60=150$.

Step2: Calculate the probability

We want to find the probability that a student plays sports given that they are passing all classes. Using the formula for conditional - probability $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $A$ is the event that a student plays sports and $B$ is the event that a student is passing all classes. Here, $n(A\cap B) = 90$ (students who play sports and pass all classes) and $n(B)=150$ (total students passing all classes). So the probability is $\frac{90}{150}$.

for second part:

Step1: List the outcomes for event B

The event B is that the sum of two dice is 8. The possible pairs are $(2,6),(3,5),(4,4),(5,3),(6,2)$, so there are 5 possible outcomes for event B.

Step2: Find the outcomes that satisfy both A and B

The event A is that the first die shows 4. Among the outcomes of event B, the pair that satisfies event A is $(4,4)$. So there is 1 outcome that satisfies both A and B.

Step3: Calculate P(A|B)

By the formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Since $P(A\cap B)=\frac{1}{36}$ (the probability of getting (4,4)) and $P(B)=\frac{5}{36}$ (probability of sum of two dice being 8), then $P(A|B)=\frac{n(A\cap B)}{n(B)}=\frac{1}{5}$.

Answer:

C. $90/150 = 0.60$