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Chapter 35: Problem 1107

Suppose that we have a bag containing two red balls, three white balls, and six blue balls. What is the probability of obtaining a red or a white ball on one withdrawal?

Short Answer

Expert verified
The probability of obtaining a red or a white ball on one withdrawal is \(\frac{5}{11}\).

Step by step solution

01

Determine the total number of balls in the bag

The bag contains 2 red balls, 3 white balls, and 6 blue balls. To find the total number of balls, simply add the numbers together: \(Total \, balls = 2 + 3 + 6 = 11\)
02

Calculate the individual probabilities

Now, we will find the probabilities of obtaining a red ball and a white ball separately. To find the probability of choosing a red ball (R), we will divide the number of red balls (2) by the total number of balls (11): \(P(R) = \frac{2}{11}\) Similarly, for the probability of choosing a white ball (W), we will divide the number of white balls (3) by the total number of balls (11): \(P(W) = \frac{3}{11}\)
03

Add the individual probabilities to get the final answer

Since we're asked to find the probability of obtaining a red or a white ball, we will add the probabilities of choosing a red ball and a white ball: \(P(R \, or \, W) = P(R) + P(W) = \frac{2}{11} + \frac{3}{11} = \frac{2+3}{11} = \frac{5}{11}\) So the probability of obtaining a red or a white ball on one withdrawal is \(\frac{5}{11}\).

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