Key Concepts: Measures of central tendency (mean, median, mode). Standard deviation measures spread. Probability of independent and dependent events. Conditional probability uses P(A|B) = P(A∩B)/P(B).
Section A: Measures of Spread
1. The dataset is: 3, 5, 7, 9, 11 [4]
(a) Calculate the mean
(b) Calculate the range
(c) Calculate the standard deviation
2. Two datasets have the same mean but different standard deviations. Interpret this difference. [2]
Section B: Probability Calculations
3. A bag contains 3 red, 4 blue, and 5 green balls. [3]
(a) Find P(red)
(b) Find P(not green)
(c) Find P(red or blue)
4. Two dice are rolled. Find the probability of: [3]
(a) Sum = 7
(b) Both dice show the same number
(c) Sum > 10
Section C: Conditional Probability
5. Cards are drawn without replacement from a standard deck. [3]
(a) Find P(2nd card is red | 1st card was red)
(b) Find P(both red)
Total marks: 20
Mark Scheme
1. (a) Mean = (3+5+7+9+11)/5 = 35/5 = 7 [1]
(b) Range = 11 - 3 = 8 [1]
(c) Variance = [(3-7)² + (5-7)² + (7-7)² + (9-7)² + (11-7)²]/5 = (16+4+0+4+16)/5 = 8; SD = √8 ≈ 2.83 [2]
2. Same mean indicates similar central value [1]; Different standard deviation means one dataset is more spread out/variable [1]
3. (a) P(red) = 3/12 = 1/4 [1]
(b) P(not green) = 7/12 [1]
(c) P(red or blue) = 7/12 [1]
4. (a) P(sum = 7) = 6/36 = 1/6 [1]
(b) P(same) = 6/36 = 1/6 [1]
(c) P(sum > 10) = 3/36 = 1/12 [1]
5. (a) P(2nd red | 1st red) = 25/51 [2]
(b) P(both red) = (26/52) × (25/51) = 25/102 [1]