Basic Probability and Frequency — Solutions
Full worked solutions, with method and final answer for every part.
Question 1
(a)The prime numbers from 1 to 10 are 2, 3, 5, 7 — four outcomes out of ten.
4/10 = 2/5
Question 2
(a)Expected frequency = probability × number of trials.
(1/6) × 300 = 50
Question 3
(a)Probabilities of an event and its complement sum to 1.
1 − 0.35 = 0.65
Question 4
(a)Expected frequency = probability × number of trials.
0.2 × 150 = 30
Question 5
(a)3 of the 6 outcomes (2,4,6) are even.
3/6 = 1/2
Question 6
(a)P(red) + P(blue) = 1, since these are the only outcomes.
1 − 3/8 = 5/8
Question 7
(a)Relative frequency = number of successes ÷ total trials.
45 ÷ 80 = 0.5625
Question 8
(a)For mutually exclusive events, P(A or B) = P(A) + P(B).
0.3 + 0.25 = 0.55
Question 9
(a)Theoretical probability is calculated from reasoning about equally likely outcomes; relative frequency is calculated from actual experimental results and estimates the true probability, converging to it as trials increase.
Theoretical probability is calculated in advance; relative frequency is measured from actual trials
Question 10
(a)MATHEMATICS has 11 letters, with M appearing twice.
2/11
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