Question

solve this problem ​

Answer 1

Answer:

(a) 0.50

(b) 0.33

(c) 0.50

(d) 0.167

Step-by-step explanation:

The sample space of rolling a die is:

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

(a)

The sample space of selecting a number less than 4 is:

S = {1, 2, 3}

Compute the probability of getting a number less than 4 as follows:

$P(Number\ less\ than\ 4)=\frac{Fvaorable\ outcomes}{Total\ outcomes}=\frac{3}{6} =0.50$

Thus, the probability of getting a number less than 4 is 0.50.

(b)

Composite numbers are positive numbers formed by the multiplication of another two smaller positive numbers.

The sample space of composite number is:

S = {4, 6}

Compute the probability of getting a composite number as follows:

$P(Composite\ number)=\frac{Fvaorable\ outcomes}{Total\ outcomes}=\frac{2}{6} =0.33$

Thus, the probability of getting a composite number is 0.33.

(c)

The sample space of numbers not less than 3 is:

S = {4, 5, 6}

Compute the probability of getting a number not less than 3 as follows:

$P(Number\ more\ than\ 3)=\frac{Fvaorable\ outcomes}{Total\ outcomes}=\frac{3}{6} =0.50$

Thus, the probability of getting a number not less than 3 is 0.50.

(d)

Perfect numbers are those numbers that can be obtained by the sum of their positive factors.

The number 6 is the first perfect number.

Express 6 as the sum of its factors as follows:

6 = 1 + 2 + 3

The sample space of perfect numbers is:

S = {6}

Compute the probability of getting a perfect number as follows:

$P(Perfect\ number)=\frac{Fvaorable\ outcomes}{Total\ outcomes}=\frac{1}{6} =0.167$

Thus, the probability of getting a perfect number is 0.167.