Theory question 105
ProbabilityA die was rolled a number of times. The outcomes are as shown in the table.
Number: 1, 2, 3, 4, 5, 6
Outcomes: 32, m, 25, 40, 28, 45
If the probability of obtaining 2 is 0.15, find the: (a) value of m; (b) number of times the die was rolled; (c) probability of obtaining an even number.
Show the model answer
Model answer
(a) m/(170 + m) = 0.15 → m = 25.5 + 0.15m → 0.85m = 25.5 → m = 30
(b) Total = 170 + 30 = 200 rolls
(c) Even outcomes = 30 + 40 + 45 = 115
P(even) = 115/200 = 23/40
Explanation
The known outcomes add up to 170; the total is 170 + m.