Question

Seven ping-pong balls numbered 1-7 are put in a hat. Three balls are chosen without replacement. What is the probability that all three numbers are even numbers?

Answer 1

probability of 1st number being even : 3/7
probability of 2nd number being even : 2/6
probability of 3rd number being even : 1/5

probability of all 3 numbers being even : 3/7 * 2/6 * 1/5 = 6/210 = 1/35

Answer 2

The probability that all three numbers are even numbers is:

`(1)/(35)`

Explanation:

There are seven balls numbered as: 1-7

and the number of even numbers are: 3 ( i.e. 2,4 and 6 )

Three balls are chosen without replacement.

Hence, the probability that all three numbers are even numbers is given by:

Ratio of number of favorable outcomes to the total number of outcomes.

Hence, the probability is:

`P(All\ three\ even\ numbers)=(3_C_3)/(7_C_3)`

where the numerator represents that the balls drawn have even numbers.

and the denominator denote the choosing of 3 balls out of a total of 7 balls.

Hence, the probability is:

`P(All\ three\ even\ numbers)=(1)/(35)`