Question

question 37
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a bag contains 4 red balls, 3 blue balls and 5 green balls. a ball is drawn at random. given that the ball drawn is not red, what is the probability that it is blue
o a. ( \frac{3}{7} )
o b. ( \frac{1}{4} )
o c. ( \frac{3}{8} )
o d. none of these
o e. ( \frac{3}{12} )

Explanation:

Step1: Calculate total non - red balls

Total number of non - red balls = Number of blue balls + Number of green balls.
Number of blue balls \(n(B)=3\), number of green balls \(n(G) = 5\). So, \(n(\text{non - red})=3 + 5=8\).

Step2: Use the formula for conditional probability

The formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the case of equally - likely outcomes, if \(A\) is the event of drawing a blue ball and \(B\) is the event of drawing a non - red ball, \(P(\text{blue}|\text{non - red})=\frac{n(\text{blue})}{n(\text{non - red})}\).
Since \(n(\text{blue}) = 3\) and \(n(\text{non - red})=8\), the probability \(P=\frac{3}{8}\).

Answer:

C. \(\frac{3}{8}\)