Answer:
a) The probability of rolling a 6 n times is [tex]=(\frac{1}{6})^n[/tex].
b) The probability of rolling a 6 five times in a row [tex]=\frac{1}{7776}[/tex]
c) The Probability of flipping heads on a coin five times in a row [tex]=\frac{1}{32}[/tex]
Step-by-step explanation:
Given : The probability of rolling a 6 on a number cube is [tex]\frac{1}{6}[/tex].
The probability of rolling a 6 twice is [tex](\frac{1}{6})^2=\frac{1}{36}[/tex].
To find :
a.) Write an expression that represents the probability of rolling 6 n times in a row.
The probability of rolling a 6 on a number cube is [tex]\frac{1}{6}[/tex].
The probability of rolling a 6 twice is [tex](\frac{1}{6})^2=\frac{1}{36}[/tex].
So,The probability of rolling a 6 n times is [tex](\frac{1}{6})^n[/tex].
b.) What is the probability of rolling a 6 five times in a row?
Substitute n=5 in part (a)
[tex](\frac{1}{6})^n[/tex]
[tex]=(\frac{1}{6})^5[/tex]
[tex]=\frac{1}{7776}[/tex]
c.) What is the probability of flipping heads on a coin five times in a row?
Coin has two sides
Probability of getting heads is [tex]\frac{1}{2}[/tex].
Probability of flipping heads on a coin five times in a row
[tex]\frac{1}{2}^5[/tex]
[tex]=\frac{1}{32}[/tex]
