Answer:
The game is fair.
Step-by-step explanation:
We are given that a board game is played as follows; a number cube numbered 1 to 6 is rolled.
Total cases=6
If the number 1 comes up , then you get nothing
Number of favourable cases that you get nothing =1
The probability that you get nothing =[tex]\frac{1}{6}=0.167[/tex]
Using of probability formula : P(E)=[tex]\frac{Number\;of\;favourable\;cases}{Total\;number\;of\;cases}[/tex]
If number 2,3 or 5 comes up you win 40 points
Number of favourable cases that you wins=3
The probability that you wins =[tex]\frac{3}{6}=0.5[/tex]
Therefore, total number of points that you get =[tex]0.5\times 40=20[/tex]
If number 4 or 6 comes up then you lose 60 points
Number of favourable cases that you lose=2
The probability that you lose =[tex]\frac{2}{6}=0.3[/tex]
Therefore, total number of points that you get =[tex]0.3\times 60=18[/tex]
Therefore, the probability of winning is greater than the probability of lose or you get nothing and the point that you get is greater than the points you lose.
Hence , the game is fair.
