Theory question 104
ProbabilityThe table shows the outcome when a die is thrown a number of times.
Scores: 1, 2, 3, 4, 5, 6
Frequency: 25, 30, x, 28, 40, 32
If the probability of obtaining a 3 is 0.225: (a) how many times was the die thrown? (b) calculate the probability that a trial chosen at random gives a score of an even number or a prime number.
Show the model answer
Model answer
(a) Total = 155 + x; x/(155 + x) = 0.225 → x = 0.225 × 155/0.775 = 45
The die was thrown 155 + 45 = 200 times.
(b) Even or prime scores are 2, 3, 4, 5, 6 (every score except 1)
Frequency = 200 − 25 = 175 → probability = 175/200 = 7/8
Explanation
Count each score once, even though 2 is both even and prime.