A bin contains 4 red balls and 9 blue balls. Several balls are drawn from the bin. Given that the 6th ball drawn is blue, what is the probability that the 8th ball drawn is red?
Answers
Answer:
Step-by-step explanation:
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Given A bin contains 4 red balls and 9 blue balls.
Several balls are drawn from the bin.
Given that the 6th ball drawn is blue,
To Find : the probability that the 8th ball drawn is red
Solution:
Red = 4
Blue = 5
Case is like this :
1 2 3 4 5 B 7 R
So we have 6 balls before 8
R = max 3 ( as 4th red has to be at 8th place ) and Blue = 8 available
out of 3 red 0 , 1 , 2 or 3 can be selected before 8th
case 1 : 0 Red 6 blues = ( ⁸C₆.³C₀/¹¹C₆) * (4/6) = (28/462) (4/6)
case 2 : 1 Red , 5 Blues = ( ⁸C₅.³C₁/¹¹C₆) * (3/6) = (168/462) (3/6)
Case 3 : 2 Red 4 blues = ( ⁸C₄.³C₂/¹¹C₆) * (2/6) = (210/462) (2/6)
case 4 : 3 Red 3 Blues = ( ⁸C₃.³C₃/¹¹C₆) * (1/6) = (56/462) (1/6)
(28/462) (4/6) + (168/462) (3/6) + (210/462) (2/6) + (56/462) (1/6)
(112 + 504 + 420 + 56) / (2772)
= (1092) /2772
= 13/33
= 0.394
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