If I pull out 7 marbles at once from a bag of 25 marbles which contained 15 green 2 red 5 purples and 3 blacks what could those marbles be
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Answer:
Let R={5 red marbles } and B=(3 black marbles }
For at least one of the three marbles drawn be black, if the first marble is red, then thefollowing three conditions will be followed.
(i) Second marble is black and third is red (E
1
)
(ii) Second marble is black and third is also black (E
2
)
(iii) Second marble is red and third is black (E
3
)
P(E
1
)=P(R
1
)⋅P(B
1
/R
1
)⋅P(R
2
/R
1
B
1
)=
8
5
⋅
7
3
⋅
6
4
=
336
60
=
28
5
P(E
2
)=P(R
1
)⋅P(B
1
/R
1
)⋅P(B
2
/R
1
B
1
)=
8
5
⋅
7
3
⋅
6
2
=
336
30
=
56
5
And P(E
3
)=P(R
1
)⋅P(R
2
/R
1
)⋅P(B
1
/R
1
R
2
)=
8
5
⋅
7
4
⋅
6
3
=
336
60
=
28
5
∴P(E)=P(E
1
)+P(E
2
)+P(E
3
)=
28
5
+
56
5
+
28
5
=
56
10+5+10
=
56
25
Step-by-step explanation:
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