Answer:
[tex]Probability = 23.3\%[/tex]
Step-by-step explanation:
Given
Number cube
Toss = 8
Required
Probability of not landing on 3
First we need to get the probability of landing on 3 in a single toss;
For a number cube;
[tex]n(3) = 1[/tex] and [tex]n(Total) = 6[/tex]
So; the probability is
[tex]P(3) = \frac{1}{6}[/tex]
First we need to get the probability of not landing on 3 in a single toss;
Opposite probability = 1;
So:
[tex]P(3) + P(3') = 1[/tex]
Make P(3') the subject of formula:
[tex]P(3') = 1 - P(3)[/tex]
[tex]P(3') = 1 - \frac{1}{6}[/tex]
[tex]P(3') = \frac{5}{6}[/tex]
In 8 toss, the required probability is
[tex]Probability = (P(3'))^8[/tex]
This gives
[tex]Probability = (\frac{5}{6})^8[/tex]
[tex]Probability = \frac{390625}{1679616}[/tex]
[tex]Probability = 0.23256803936[/tex]
Convert to percentage
[tex]Probability = 23.256803936\%[/tex]
Approximate to 1 decimal place:
[tex]Probability = 23.3\%[/tex]
