a bag contains 3 red balls and 4 white balls find the probability distribution of the number of red balls in 3 drawers with replacement
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Answered by
1
Answer:
12
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Answered by
2
Answer:
Three bals are taken out of an urn
Sample space is
=S(RRR,RRW,RWR,WRR,RWW,WRW,WWR,WWW)
Where R represents red ball and W, white ball
Let X= number of red balls.
so possible value of X are 3,2,1,2,1,0 or 0,1,2,3 (no red ball)
P(X=0)=P(No red ball)=P(WWW)
=
7
4
×
6
3
×
5
2
[∵ P(R)=
7
3
(P(W)=
7
4
)]
=
35
4
P(X=1)=P(RWW,WRW,WWR)=P(RWW)+P(WRW)+P(WWR)
=
7
3
×
6
4
×
5
3
+
7
4
×
6
3
×
5
3
+
7
4
×
6
3
×
5
3
=
35
6
+
35
6
+
35
6
=
35
18
P(X=2)=P(RRW,RWR,WRR)=P(RRW)+P(RWR)+P(WRR)
=
7
3
×
6
2
×
5
4
+
7
3
×
6
4
×
5
2
+
7
4
×
6
3
×
5
2
=
35
4
+
35
4
+
35
4
=
35
12
Required probability distribution
X 0 1 2 3
P(X)
35
4
35
18
35
12
35
1
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