Case Study Based Questions
I. A bag contains 6 red, 8 green, 9 blue and 4 yellow balls. One ball is drawn at random.
Q1: The probability that the ball drawn is blue, is:
Step 1: Calculate the total number of balls in the bag.
\[
\text{Total balls} = 6 + 8 + 9 + 4 = 27
\]Step 2: Identify the number of favorable outcomes (blue balls).
\[
\text{Number of blue balls} = 9
\]Step 3: Calculate the probability \( P \) of drawing a blue ball.
\[
P(\text{blue}) = \frac{\text{Number of blue balls}}{\text{Total number of balls}} = \frac{9}{27} = \frac{1}{3}
\]Answer: a. \( \frac{1}{3} \)
Q2: The probability that the ball drawn is either red or blue, is:
Step 1: Calculate the total number of balls.
\[
\text{Total balls} = 6 + 8 + 9 + 4 = 27
\]Step 2: Calculate the number of favorable outcomes (red or blue balls).
\[
\text{Number of red balls} = 6, \quad \text{Number of blue balls} = 9 \\
\text{Total favorable outcomes} = 6 + 9 = 15
\]Step 3: Calculate the probability \( P \) of drawing a red or blue ball.
\[
P(\text{red or blue}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of balls}} = \frac{15}{27} = \frac{5}{9}
\]Answer: c. \( \frac{5}{9} \)
Q3: The probability that the ball drawn is non-green, is:
Step 1: Calculate the total number of balls.
\[
\text{Total balls} = 6 + 8 + 9 + 4 = 27
\]Step 2: Calculate the number of green balls.
\[
\text{Number of green balls} = 8
\]Step 3: Calculate the number of non-green balls.
\[
\text{Non-green balls} = \text{Total balls} – \text{Green balls} = 27 – 8 = 19
\]Step 4: Calculate the probability \( P \) of drawing a non-green ball.
\[
P(\text{non-green}) = \frac{\text{Number of non-green balls}}{\text{Total number of balls}} = \frac{19}{27}
\]Answer: c. \( \frac{19}{27} \)
Q4: The probability that the ball drawn is non-red, is:
Step 1: Calculate the total number of balls.
\[
\text{Total balls} = 6 + 8 + 9 + 4 = 27
\]Step 2: Calculate the number of red balls.
\[
\text{Number of red balls} = 6
\]Step 3: Calculate the number of non-red balls.
\[
\text{Non-red balls} = \text{Total balls} – \text{Red balls} = 27 – 6 = 21
\]Step 4: Calculate the probability \( P \) of drawing a non-red ball.
\[
P(\text{non-red}) = \frac{\text{Number of non-red balls}}{\text{Total number of balls}} = \frac{21}{27} = \frac{7}{9}
\]Answer: a. \( \frac{7}{9} \)
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