An individual is handover a bag filled with balls of different colours. The table below gives the probability that a randomly chosen ball is of a specific colour,along with a missing probability value of picking a ball of white colour Red=0.2 Yellow=0.2 Green=0.1 Orange=0.1 Blue=0.3 White=?
Answers
A bag contains 5 white balls, 6 red balls and 9 green balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is :
(i) a green ball.
(ii) a white or a red ball.
(iii) is neither a green ball nor a white ball.
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Class 12
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>>A bag contains 4 balls.Two ...
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A bag contains 4 balls.Two balls drawn at random without replacement and are found to be white. What is the probability that all balls are white?
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Solution
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Let A be the event of drawing 2 white balls.
from the bag containing 4 balls.
The remaining 2 balls of the bag has three options.
Let E
1
be the event that the remaining 2 balls of the bag are not white
Let E
2
be the event that are remaining 2 balls of the bag are one white and one not white.
Let E
3
be the event that rae remaining 2 balls of the bag are white.
∴P(E
1
)=P(E
2
)=P(E
3
)=
3
1
P(A/E
1
)=P (drawing 2 white balls from the bag contains 2 white and 2 not white)
=
4
C
2
2
C
2
=
6
1
P(A/E
2
)=P (drawing 2 white balls from the bag containing 2 white and 1 non-white)
=
3
.C
2
/
4
.C
2
=
6
3
=
2
1
P(A/E
3
)=P (drawing 2 white ball from bag containing 4 whire balls)
= 1.
P(E
2
/A)=
P(E
1
)P(A/E
1
)+P(E
2
)+P(E
3
)P(A/E
3
)
P(E
2
)(PA/E
2
)
=
3
1
×
6
1
+
3
1
×
2
1
+
3
1
.
1
1
=
3
1
(
6
1
+
2
1
+1)
=
3
1
P(E
2
/A)=
3
1
.
3
5
3
1
.
2
1
=
9
5
6
1
=
6
1
×
5
3
=
10
3