Question

A box contains 12 balls numbered 1 through 12. Two balls are drawn in succession without replacement. If the second ball has the number 4 on​ it, what is the probability that the first ball had a smaller number on​ it? An even number on​ it? The probability that the first ball had a smaller number is nothing.

Answer 1

Answer with explanation:

A box contains 12 balls numbered 1 through 12.

Also the ball are drawn without replacement.

a)

The probability that the first ball had a smaller number on​ it.

i.e. the number on the first ball could be: {1,2,3}

Hence, the probability  that the first ball had a smaller number on​ it is:

              $\dfrac{3}{12}=\dfrac{1}{4}=0.25$

b)

The probability that the first ball has a even number on it is:

There are total 6 even numbers {2,4,6,8,10,12}

but 4 can't be considered as it comes on the second draw, so we are left with just 5 balls with even number.

Hence, the probability is:

$\dfrac{5}{12}=0.4166$