A box contains 4 red balls, 5 green balls and 6 black balls. 6 balls are selected at random from the box.
Find a probability distribution for green balls. Calculate mean and variance of this distribution.
Find a probability distribution for red balls. Calculate mean and variance of this distribution to
Answers
Answer
Let X denote the number of white balls in a sample of 3 balls drawn from a bag containing 4 white and 6 red balls.
Then, X can take the values 0 white ball 1 or 2 or 3 white ball.
⇒ P(X=0)=
10
C
3
6
C
3
=
3!7!
10!
3!3!
6!
=
10×9×8
6×5××4
=
720
120
=
6
1
⇒ P(X=1)=
10
C
3
4
C
1
×
6
C
2
=
3!7!
10!
1!3!
4!
×
2!4!
6!
=
10×9×8
6×5×4×3
=
720
360
=
2
1
⇒ P(X=2)=
10
C
3
4
C
2
×
6
C
1
=
3!7!
10!
2!2!
4!
×
1!5!
6!
=
120
36
=
10
3
⇒ P(X=3)=
10
C
3
4
C
3
=
3!7!
10!
3!1!
4!
=
120
4
=
30
1
X 0 1 2 3
P(X)
6
1
2
1
10
3
30
1
Step-by-step explanation:
Basic Definitions and Formulas
Formula: Profit or Gain = S.P. – C.P. Loss: If the selling price is less than the cost price, the difference between them is the loss incurred.
hope this helps you