Question

A fair die is rolled 10 times. What is the probability that an odd number (1, 3, or 5) will occur fewer than 3 times?

Answer 1

Answer:

The probability that an odd number rolls of a die for less than 3 times is 0.054.

Step-by-step explanation:

The sample space of rolling a fair die is, S = {1, 2, 3, 4, 5, 6}

The odd numbers are, {1, 3, and 5}.

The probability that an odd number occurs is:

$P(Odd)=\frac{Favorable\ outcomes}{Total\ no.\ of\ outcomes}=\frac{3}{6}=\frac{1}{2}$

The die was rolled n = 10 times.

Let X = number of rolls in which an odd number occurs.

The random variable $X\sim Bin(n=10,p=\frac{1}{2})$

The probability distribution of binomial is:

$P(X =x)={n\choose x}p^{x}(1-p)^{n-x}$

Compute the probability that an odd number will occur less than 3 times as follows:

$P(X$

Thus, the probability that an odd number rolls of a die for less than 3 times is 0.054.