Question

1. A simple random sample of the students at Hogwarts was taken. Their heritage (pure blood, half blood or muggle born) and their scores on their OWLs (Ordinary Wizarding Level) were recorded below.

	Pure Blood	Half Blood	Muggle Born	Total
Outstanding	10	10	10	30
Exceeds Expectation	30	30	45	105
Acceptable	30	95	30	155
Poor	2	40	8	50
Dreadful	23	20	2	45
Troll	5	5	5	15
Total	100	200	100	400

1. What is the probability that a wizard chosen at random from this sample will be in the Muggle Born category?

2. What is the probability that a wizard chosen at random from this sample from the Outstanding level will be in the Muggle Born category?

3. Based on the table above is being Muggle Born and receiving an Outstanding on the OWL independent? Justify your answer.

4. If heritage and scores were completely independent, find the number of pure bloods you would expect to receive a Troll on their OWL.

Answer 1

1.

The probability that a wizard chosen at random from this sample will be in the Muggle Born category =

P = n(Muggle Born ) / total no. of students

P = 100 / 400

P = 0.25

2.

the probability that a wizard chosen at random from this sample from the Outstanding level will be in the Muggle Born category

P = 10 / 400

P = 0.025

3.

Let Event A = being Muggle Born

Event B = receiving an Outstanding on the OWL

P(A) = 0.25

P(B) = 30 / 400 = 0.075

and P(A and B ) = 0.025

Here P(A) * P(B) = 0.25 * 0.075 = 0.018

hence A and B are not independent.

4.

There are 5 pure bloods, would expect to receive a Troll on their OWL