Probability and Statistical Analysis Flashcards

A bag contains 4 red, 3 blue, and 5 green marbles. If two marbles are drawn without replacement, what is the probability both are green?

Answer: 5/33

P(both green) = (5/12) × (4/11) = 20/132 = 5/33.

The median of a data set is best described as:

Answer: The middle value when data is ordered

The median is the middle value of an ordered dataset, or the average of the two middle values when the count is even.

Events A and B are mutually exclusive. P(A) = 0.35 and P(B) = 0.45. What is P(A or B)?

Answer: 0.8

For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.35 + 0.45 = 0.80.

A dataset has values: 2, 4, 4, 6, 8, 10. What is the variance?

Answer: 6.33

Mean = 34/6 ≈ 5.67; variance = [(3.67²+1.67²+1.67²+0.11²+5.45²+19.0²)/6] ≈ 6.33 (population variance).

In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

Answer: 68%

The empirical rule states that about 68% of data lies within ±1 standard deviation of the mean in a normal distribution.

A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?

Answer: 1/4

C(4,3) × (1/2)³ × (1/2)¹ = 4 × (1/16) = 4/16 = 1/4.

Which measure of central tendency is most affected by extreme outliers?

Answer: Mean

The mean is calculated using all values, so a single extreme outlier can pull it significantly away from the center of the data.