Questions: Six balls numbered from 1 to 6 are placed in a bag. Some are white and some are grey, as shown below. The balls numbered 1,2,4, and 6 are white. The balls numbered 3 and 5 are grey. Answer the following questions. Write each answer as a fraction. A ball will be randomly selected. (a) What is the probability that the selected ball is white? (b) What is the probability that the selected ball is white, given that an odd numbered ball is selected?

Six balls numbered from 1 to 6 are placed in a bag. Some are white and some are grey, as shown below. The balls numbered 1,2,4, and 6 are white. The balls numbered 3 and 5 are grey. Answer the following questions. Write each answer as a fraction. A ball will be randomly selected. (a) What is the probability that the selected ball is white? (b) What is the probability that the selected ball is white, given that an odd numbered ball is selected?
Transcript text: Six balls numbered from 1 to 6 are placed in a bag. Some are white and some are grey, as shown below. The balls numbered $1,2,4$, and 6 are white. The balls numbered 3 and 5 are grey. Answer the following questions. Write each answer as a fraction. A ball will be randomly selected. (a) What is the probability that the selected ball is white? $\square$ (b) What is the probability that the selected ball is white, given that an oddnumbered ball is selected? $\square$
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Solution

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Solution Steps

Step 1: Probability of selecting a white ball

There are 6 balls in total. The white balls are numbered 1, 2, 4, and 6. There are 4 white balls. The probability of selecting a white ball is the number of white balls divided by the total number of balls. Probability = $\frac{\text{Number of white balls}}{\text{Total number of balls}} = \frac{4}{6} = \frac{2}{3}$

Step 2: Probability of selecting a white ball given that an odd-numbered ball is selected

The odd-numbered balls are 1, 3, and 5. There are 3 odd-numbered balls. Out of these, only the ball numbered 1 is white. The probability of selecting a white ball given that an odd-numbered ball is selected is the number of white odd-numbered balls divided by the total number of odd-numbered balls. Probability = $\frac{\text{Number of white odd-numbered balls}}{\text{Total number of odd-numbered balls}} = \frac{1}{3}$

Final Answer

(a) \\(\boxed{\frac{2}{3}}\\) (b) \\(\boxed{\frac{1}{3}}\\)

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