Question

Terry has a cube numbered from 1 to 6. He tosses the cube onto the floor 120 times. How many times should he expect it to land on a 2 or 3?

Answer 1

The expected value of a dataset is the mean or average of the dataset.

The cube is expected to land on a 2 or 3 a total of 40 times

The cube is said to be numbered from 1 to 6.

This means that, the probability of getting each number is 1/6.

So, the probability that the outcome is 2 or 3 is:

$P(2\ or\ 3) = P(2) + P(3)$

This gives

$P(2\ or\ 3) = \frac 16 + \frac 16$

Add fractions

$P(2\ or\ 3) = \frac {1+1}6$

$P(2\ or\ 3) = \frac 26$

Simplify

$P(2\ or\ 3) = \frac 13$

The number of rolls (n) is 120.

So, the expected value is:

$E(x) = np$

This gives

$E(x) = 120 \times \frac 13$

$E(x) = 40$

Hence, the cube is expected to land on a 2 or 3 a total of 40 times

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