The probability that all four balls are red is 0.0050
The probability that two of the balls are red and two are blues is 0.0360
5 Red Balls and 9 Blue Balls
= Four Balls are drawn at random, without replacement
= Total Number of Balls = 5+9=14
The probability that all four balls are red =
P (all four balls are red) = ⁵C₄/¹⁴C₄
Therefore, By nCr = n! / r! (n-r)!
⁵C₄ = 5!/ 4!×(5-4)! = 5
¹⁴C₄ = 14!/ 4!×(14-4)! = 1001
P(All are red) = 5/1001 = 0.00495 = 0.005
Hence the probability that all four balls are red is 0.0050
P (Two balls are red and two balls are blue) = ⁵C₂ ×⁹C₂ / ¹⁴C₄
⁵C₂ = 5!/ 2!×(5-2)! = 10
⁹C₂ = 9!/ 2!×(9-2)! = 36
P(Two Red and Two Blue) = 10×36/1001
= 0.035964
= 0.0360
Hence, the probability that two of the balls are red and two are blue is 0.0360
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