A die was rolled a number of times. The…

Question 1 Report

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;

Answer

Number	1	2	3	4	5	6
Outcomes	32	m	25	40	28	45

Answer Details

Number	1	2	3	4	5	6
Outcomes	32	m	25	40	28	45

(a) Value of m. The total number of rolls is \(N=32+m+25+40+28+45=170+m\). Since \(P(2)=0.15\):

\[ \frac{m}{170+m}=0.15 \;\Rightarrow\; m=0.15(170+m)=25.5+0.15m \] \[ 0.85m=25.5 \;\Rightarrow\; m=30 \]

(b) Number of times the die was rolled.

\[ N=170+30=200 \]

(c) Probability of an even number. Even outcomes are 2, 4 and 6:

\[ 30+40+45=115 \] \[ P(\text{even})=\frac{115}{200}=\frac{23}{40}=0.575 \]

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...