Question

15 POINTS: The probability of rolling a 6 on a number cube is 1/6. The probability of rolling a 6 twice is (1/6)^2= 1/36. a.) Write an expression that represents the probability of rolling 6 n times in a row.

b.) What is the probability of rolling a 6 five times in a row?

c.) What is the probability of flipping heads on a coin five times in a row?

Answer 1

a) The probability of rolling a 6 n times is
`=((1)/(6))^n`.

b) The probability of rolling a 6 five times in a row
`=(1)/(7776)`

c) The Probability of flipping heads on a coin five times in a row
`=(1)/(32)`

Explanation:

Given : The probability of rolling a 6 on a number cube is
`(1)/(6)`.

The probability of rolling a 6 twice is
`((1)/(6))^2=(1)/(36)`.

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
`(1)/(6)`.

The probability of rolling a 6 twice is
`((1)/(6))^2=(1)/(36)`.

So,The probability of rolling a 6 n times is
`((1)/(6))^n`.

b.) What is the probability of rolling a 6 five times in a row?

Substitute n=5 in part (a)

`((1)/(6))^n`

`=((1)/(6))^5`

`=(1)/(7776)`

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
`(1)/(2)`.

Probability of flipping heads on a coin five times in a row

`(1)/(2)^5`

`=(1)/(32)`