Question

an bag contains 5 pink balls, 10 purple balls, and 2 white balls. three balls are selected, one after the other, without replacement. find the probability that all three balls are purple. express your answer as a decimal, rounded to the nearest hundredth.

Explanation:

Step1: Calculate total number of balls

Total balls = \(5 + 10+2=17\)

Step2: Calculate probability for first - draw

Probability of first - ball being purple: \(P_1=\frac{10}{17}\)

Step3: Calculate probability for second - draw

After first draw (no replacement), total balls = \(16\), purple balls = \(9\). So \(P_2=\frac{9}{16}\)

Step4: Calculate probability for third - draw

After second draw (no replacement), total balls = \(15\), purple balls = \(8\). So \(P_3=\frac{8}{15}\)

Step5: Calculate combined probability

Using multiplication rule for dependent events: \(P = P_1\times P_2\times P_3=\frac{10}{17}\times\frac{9}{16}\times\frac{8}{15}\)

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Answer:

\(0.18\)