Question

A peculiarly weighted six sided die has the following probability model:

X = die face	1	2	3	4	5	6
Probability	0.14	0.10	0.17	0.16	0.24	?

What is the probability of rolling a 6 on this die?

Answer 1

Let X be the random variable which represents the number that appear on the face of weighted six sided die.

The possible number that can occur on the face of six sided die be 1, 2, 3, 4, 5, 6. We have given certain probability which is as follows

P(X=1)=0.14.

P(X=2)=0.10.

P(X=3)=0.17.

P(X=4)=0.16.

P(X=5)=0.24.

Let a be the probability that X acquire value 6, so P(X=6)=a.Then we know that the sum of all the probability over the sample space is 1. Therefore, we have

Therefore, we have

P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)=1.

This gives

0.14+0.10+0.17+0.16+0.24+a=1.

0.81+a=1.00

Therefore, a=1.00-0.81=0.19

Therefore, the probability is 0.19 of rolling a six on the die.