Question

there are 4 sets of balls numbered 1 through 9 placed in a bowl. If 4 balls are randomly chosen without replacement, find the probability that the balls have the same number. Express your answer as a fraction

Answer 1

Explanations:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

If there are 4 sets of balls numbered 1 through 9 placed in a bowl, the total outcome will be (4*9) = 36 balls (36 balls in total with each number appearing four times.)

If we pick the first ball without replacing it, there will be 35 balls left with 3 of the remaining balls having the same number as the selected ball.

Pr(remaining 3 equal balls) = 3/35

Similarly, if we pick 3 equal balls, there is now a single equal ball left out of 33 balls in the bowl. The probability of picking 4 equal balls is:

`\begin{gathered} \text{ Pr(4 equal balls) = }(3)/(35)*(1)/(33) \\ \text{ Pr(4 equal balls) = }(1)/(35*11) \\ \text{ Pr(4 equal balls) = }(1)/(385) \end{gathered}`