Question

You have 6 chips numbered 1 through 6 in a cup. You pull one out, then another one out without replacing the first one. What is the probability of picking 5 and 3

Answer 1

The probability of two events happening one after another is the product of the individual probabilities for each event.

There are two possible ways of picking 5 and 3: picking 5 and then 3, or picking 3 and then 5.

The probability of picking the number 5 from a set of 6 chips is:

$\frac{1}{6}$

The probability of picking a 3 from the set of the remaining 5 chips, is:

$\frac{1}{5}$

Then, the probability of picking a 5 and then a 3 is:

$\frac{1}{6}\times\frac{1}{5}=\frac{1}{30}$

Similarly, the probability of picking a 3 and then a 5 is 1/30.

Since any of these cases is a valid outpit, then the total probability of picking 5 and 3 would be:

$\frac{1}{30}+\frac{1}{30}=\frac{2}{30}=\frac{1}{15}$

Therefore, the probability of picking 5 and 3 is:

$\frac{1}{15}$