NSAA Mathematics - Statistics and Probability Flashcards

A bag contains 4 red, 3 blue, and 5 green balls. What is the probability of drawing a blue ball?

Answer: 1/4

P(blue) = 3/(4+3+5) = 3/12 = 1/4.

The mean of five numbers is 8. If four of the numbers are 6, 7, 9, and 10, what is the fifth number?

Answer: 8

Total sum = 5 × 8 = 40; sum of four = 32; fifth = 40 - 32 = 8.

A die is rolled twice. What is the probability of getting a 6 on both rolls?

Answer: 1/36

P(6 on both) = 1/6 × 1/6 = 1/36 (independent events).

The median of the data set {3, 7, 9, 2, 5} is:

Answer: 5

Sorted: {2, 3, 5, 7, 9}; middle value = 5.

What is the variance of the set {2, 4, 6} given mean = 4?

Answer: 4

Using sample variance (n-1): [(2-4)²+(4-4)²+(6-4)²]/(3-1) = 8/2 = 4.

If events A and B are mutually exclusive, what is P(A or B)?

Answer: P(A) + P(B)

For mutually exclusive events, P(A∩B) = 0, so P(A or B) = P(A) + P(B).