Question

A random number generator on a computer selects two integers from 1 through 40. What is the probability that (a) both numbers are even, (b) one number is even and one number is odd, (c) both numbers are less than 30, and (d) the same number is selected twice?

Answer 1

Answer:

(a) 0.25

(b) 0.5

(c) 0.5256

(d) 0.025

Step-by-step explanation:

(a) There are 20 even numbers out of 40 the probability that both numbers are even is:

$P=\frac{20}{40} *\frac{20}{40} =\frac{1}{4}=0.25$

(b) The events for which one number is even and one number is odd are:

- First is odd, second is even

- First is even, second is odd.

The probability is:

$P = \frac{20}{40}*\frac{20}{40}+\frac{20}{40}*\frac{20}{40}=\frac{1}{2}=0.5$

(c) There are 29 numbers that are less than 30, the probability that both numbers are less than 30 is:

$P=\frac{29}{40}*\frac{29}{40}=\frac{841}{1600}=0.5256$

(d) If any number from 1 to 40 is selected in the first pick, the probability that the same number is selected again is:

$P=\frac{1}{40} =0.025$