A 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.
Explanation
Pr(2) = 0.15
\(\frac{m}{32 + m + 25 + 40 + 28 + 45}\) = 0.15
\(\frac{m}{m + 170}\) = 0.15
m = 0.15(m + 170)
m = 0.15m + 25.5
m - 0.15m = 25.5
\(\frac{0.85m}{0.85} = \frac{25.5}{0.85}\)
m = 30
(b) Number of time
= 32 + 30 + 25 + 40 + 28 + 45
= 200 times
(c) Pr(even number) = \(\frac{30 + 40 + 45}{200}\)
= \(\frac{115}{200}\)
= \(\frac{23}{40}\)