Question

A die is thrown 5 times. What is the probability of obtaining a 4 or 5?

A. Zero

B. Once

C. Twice

Hint: Calculate the p(4 or 5) for a single throw

Answer 1

The probability of a single throw is

$p=\frac{2}{6}=\frac{1}{3}$

Then

$A:P=\left( 1-p \right) ^5=\left( \frac{2}{3} \right) ^5=\frac{32}{243}\\B:P=5p\left( 1-p \right) ^4=5\cdot \frac{1}{3}\left( \frac{2}{3} \right) ^4=\frac{80}{243}\\C:P=C_{5}^{2}p^2\left( 1-p \right) ^3=10\cdot \left( \frac{1}{3} \right) ^2\left( \frac{2}{3} \right) ^3=\frac{80}{243}$