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

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Answer:

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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:

[tex]\begin{gathered} \text{ Pr(4 equal balls) = }\frac{3}{35}\times\frac{1}{33} \\ \text{ Pr(4 equal balls) = }\frac{1}{35\times11} \\ \text{ Pr(4 equal balls) = }\frac{1}{385} \end{gathered}[/tex]

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