Question

A pair of fair dice is cast. What is the probabiliy that at least one of the numbers falling uppermost is a 1

Answer 1

Answer:

The probability that at least one of the numbers falling uppermost is a 1 is $\frac{11}{36}$

Step-by-step explanation:

If a pair of fair dice, lets say diceA and diceB, is cast:

At least one of the numbers falling uppermost is a 1 can happen in three different ways:

1. both are 1
2. diceA is 1 and diceB is not 1
3. diceA is not 1 and diceB is 1

We should calculate all the 3 probabilities and sum them up.

1) $\frac{1}{6} *\frac{1}{6}$ = $\frac{1}{36}$

2) $\frac{1}{6} *\frac{5}{6}$ = $\frac{5}{36}$

3) $\frac{5}{6} *\frac{1}{6}$ = $\frac{5}{36}$

Then the probability that at least one of the numbers falling uppermost is a 1 is:

$\frac{1}{36} +\frac{5}{36} +\frac{5}{36} =\frac{11}{36}$