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.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
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) = \(\frac{30 + 40 + 45}{200}\)
= \(\frac{115}{200}\)
= \(\frac{23}{40}\)
Source: Myschool Past Questions Archive (Record #58710)