Question

A child has nine cards numbered 1 through 9. The child places three cards in a row to form a three-digit number. Find the probability that the number is larger than 800. (Round your answer to three decimal places.)

Answer 1

Answer: 0.222

Explanation:

The numerator of the probability is the number of ways a child can succeed in picking a number greater than 800

There are 2 ways a child can pick the first digit as 8 or 9
That leaves 8 ways the child pick the second digit.
That leaves 7 ways the child can pick the third digit.

So there are 2·8·7 = 112 ways the child can pick a number larger than 800.

The denominator of the probability is the number of ways the child can pick any number whether smaller or larger than 800.

There are 9 way the child can pick the first digit.
That leaves 8 ways the child can pick the second digit.
That leaves 7 ways the child can pick the third digit.
 
So there are 9·8·7 ways = 504 ways to pick any number smaller or greater than 800

So the probability of picking a number greater than 800 is given as