A box contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random,
Practice Questions
Q1
A box contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue given that it is not red?
1/2
1/4
1/3
1/5
Questions & Step-by-Step Solutions
A box contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue given that it is not red?
Correct Answer: 3/5
Step 1: Count the total number of balls in the box. There are 5 red, 3 blue, and 2 green balls.
Step 2: Calculate the total number of balls: 5 (red) + 3 (blue) + 2 (green) = 10 balls.
Step 3: Identify the balls that are not red. These are the 3 blue and 2 green balls.
Step 4: Count the number of balls that are not red: 3 (blue) + 2 (green) = 5 balls.
Step 5: Determine how many of the non-red balls are blue. There are 3 blue balls.
Step 6: Calculate the probability of drawing a blue ball given that it is not red. This is the number of blue balls divided by the total number of non-red balls: 3 (blue) / 5 (not red) = 3/5.
Step 7: Write the final answer: The probability that the ball is blue given that it is not red is 3/5.
Conditional Probability – The probability of an event occurring given that another event has already occurred.
Total Probability – Understanding the total number of outcomes relevant to the condition specified.
