Question

A standard number cube has 6 sides labeled 1 to 6. apu rolls a standard number cube 30 times. How many times can

Answer 1

Answer:

The expected value of rolling a 5 or 6 is 10.

Step-by-step explanation:

The sample space of rolling a standard number cube is:

S = {1, 2, 3, 4, 5 and 6}

The cube is standard, this implies that each side has an equal probability of landing face-up.

So, the probability of all the six outcomes is same, i.e. $\frac{1}{6}$.

Now it is provided that Apu rolls the cube n = 30 times.

Let the random variable X represent the value on the face of cube.

The event of rolling a 5 and rolling a 6 are mutually exclusive, i.e. they cannot occur together.

So, P (X = 5 and X = 6) = 0.

Compute the probability of getting a 5 or 6 as follows:

P (X = 5 or X = 6) = P (X = 5) + P (X = 6) - P (X = 5 and X = 6)

                            = P (X = 5) + P (X = 6)

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

Compute the expected value of rolling a 5 or 6 as follows:

$E(X = 5\ \text{or}\ X = 6)=n\times P(X = 5\ \text{or}\ X = 6)$

                               $=30\times \frac{1}{3}\\\\=10$

Thus, the expected value of rolling a 5 or 6 is 10.