Questions: Chapter 8 Question 5 A ball is drawn randomly from a jar that contains 6 red balls, 4 white balls, and 7 yellow balls. Find the probability of the given event. Write your answers as reduced fractions or whole numbers. (a) P(A red ball is drawn) = (b) P(The ball drawn is NOT red) = (c) P(A green ball is drawn) =

Solution Steps

To solve the given probability questions, we need to follow these steps:

1. Total Number of Balls: Calculate the total number of balls in the jar.
2. Probability of Drawing a Red Ball: Use the formula for probability, which is the number of favorable outcomes divided by the total number of outcomes.
3. Probability of Drawing a Non-Red Ball: Subtract the probability of drawing a red ball from 1.
4. Probability of Drawing a Green Ball: Since there are no green balls in the jar, the probability is 0.

The total number of balls in the jar is calculated as follows: \[ \text{Total Balls} = \text{Red Balls} + \text{White Balls} + \text{Yellow Balls} = 6 + 4 + 7 = 17 \]

The probability of drawing a red ball \( P(A) \) is given by the ratio of the number of red balls to the total number of balls: \[ P(A \text{ red ball is drawn}) = \frac{\text{Red Balls}}{\text{Total Balls}} = \frac{6}{17} \approx 0.3529 \]

The probability of drawing a ball that is not red \( P(B) \) can be calculated as: \[ P(\text{The ball drawn is NOT red}) = 1 - P(A) = 1 - \frac{6}{17} = \frac{11}{17} \approx 0.6471 \]

Since there are no green balls in the jar, the probability of drawing a green ball \( P(C) \) is: \[ P(A \text{ green ball is drawn}) = \frac{\text{Green Balls}}{\text{Total Balls}} = \frac{0}{17} = 0.0 \]

Final Answer