Chapter 6.1, Problem 63E

a.

To determine

To find: The expression for the probability of rolling a 6 for n times in a row.

Answer to Problem 63E

  ${\left(\frac{1}{6}\right)}^n$

Explanation of Solution

Given information:Given information: The probability of rolling a 6 on a number cube is $\frac{1}{6}$. The probability of rolling a 6 twice in a row is ${\left(\frac{1}{6}\right)}^2$.

Calculation:

When a cube rolled for ‘ n’ times which give

  $\frac{1}{6}*\frac{1}{6}*\frac{1}{6}*\mathrm{....}$ n times.

Simplify it,

  ${\left(\frac{1}{6}\right)}^n$

b.

To determine

To find: The probability of rolling a 6 four times in a row.

Answer to Problem 63E

The probability of rolling a 6 four times is $\frac{1}{1296}$

Explanation of Solution

Given information:Rolling a number cube for 4 times.

Calculation:

When rolling the number cube for 4 times, the probability of 6 for four times is $\frac{1}{6}*\frac{1}{6}*\frac{1}{6}*\frac{1}{6}$

It is simplified to

  $\frac{1}{6}*\frac{1}{6}*\frac{1}{6}*\frac{1}{6}=\frac{1}{1296}$

c.

To determine

To find: The probability to get heads on coin when flip for 5 times.

Answer to Problem 63E

The probability of getting heads when flip a coin for 5 times is $\frac{1}{32}$

Explanation of Solution

Given information: Flipping a coin for 5 times.

Calculation:

When flip a coin it shows either Tail or Head. So, probability of getting head $=\frac{1}{2}$

So, when it flipped for 5 times, the probability is $\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}$

Simplify it,

  $\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}=\frac{1}{32}$