Question

A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and third balls drawn are red is _________ (round off to two decimal places)

Hint:

When drawing without replacement, the probability of successive events changes based on the remaining items in the sample space.

Answer 1

Correct Answer: 0.32

The probability of drawing a red ball in succession without replacement is given by multiplying the probabilities for each draw. The total number of balls is 10. The events are: 1. The probability that the second ball is red: Since one ball is already drawn, the total number of balls left is 9, and the number of red balls left is 5. So, the probability is: \[ P(\text{2nd ball red}) = \frac{5}{9}. \] 2. The probability that the third ball is red, given the second was red: Now, the total number of balls left is 8, and the number of red balls left is 4. So, the probability is: \[ P(\text{3rd ball red}) = \frac{4}{8} = \frac{1}{2}. \] The total probability is the product of the individual probabilities: \[ P(\text{2nd and 3rd balls red}) = \frac{5}{9} \times \frac{1}{2} = \frac{5}{18} \approx 0.32. \] Thus, the probability that the second and third balls drawn are red is \( 0.32 \).