3 balls are randomly chosen from an urn containing 3 White,3 Red and 4 Black balls. Suppose that we win Rs.1 for each white ball selected & lose Rs.1 for each red ball selected . Then write the probability distribution for total winning amount from the experiment
Answers
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probability distribution for total winning amount from the experiment
Step-by-step explanation:
3 - White
3 - Red
4 - Black
P (-3) means all 3 Red balls = ³C₃/¹⁰C₃ = 1/120
P (-2) means 2 Red balls 1 Black Balls = ³C₂ * ⁴C₁/¹⁰C₃ = 12/120 = 1/10
P (-1) means 1 Red balls 2 Black Balls or 2 Red 1 White Balls
= (³C₁ * ⁴C₂ + ³C₂ * ³C₁)/¹⁰C₃ = 27/120 = 9/40
P (0) means all 1 Red balls 1 White 1 Black Balls or 3 Black Balls
= (³C₁ * ³C₁*⁴C₁ + ⁴C₃)/¹⁰C₃ =40/120 = 1/3
P (1) means 1 White balls 2 Black Balls or 1 Red 2 White Balls
= (³C₁ * ⁴C₂ + ³C₂ * ³C₁)/¹⁰C₃ = 27/120 = 9/40
P (2) means 2 White balls 1 Black Balls = ³C₂ * ⁴C₁/¹⁰C₃ = 12/120 = 1/10
P (3) means all 3 White balls = ³C₃/¹⁰C₃ = 1/120
Winning Probability
-3 1/120
-2 1/10
-1 9/40
0 1/3
1 9/40
2 1/10
3 1/120
(-3)(1/120) + (-2)(1/10) + (-1)(9/40) + 0 + 1(9/40) + 2(1/10) + 3(1/120)
= 0
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