Final answer:
The probability of drawing 2 blue balls and 1 red ball in sequence from a bag with 4 blue, 6 white, and 5 red balls without replacement is 0.0823.
Step-by-step explanation:
To find the probability of drawing 2 blue balls and 1 red ball from a bag containing 4 blue, 6 white, and 5 red balls without replacement, we can use the concept of combinatorial probability. Since the balls are drawn without replacement, the probabilities will change after each draw.
The probability of drawing the first blue ball is 4/15 (since there are 4 blue balls out of 15 total balls). After drawing one blue ball, there are now 3 blue balls and 14 total balls, so the probability of drawing a second blue ball is 3/14. Finally, after two blue balls have been drawn, there are 5 red balls out of 13 total balls remaining, so the probability of drawing a red ball is 5/13.
To find the combined probability of all three events occurring in sequence (two blue balls and then one red ball), we multiply the probabilities of each event:
(4/15) × (3/14) × (5/13) = 0.0823
The correct answer is (b) 0.0823.