A bag contains 15 balls of which x are blue and the remaining are red. If the number or red balls are increased by 5, the probability of red balls are increased by 5, the probability of drawing the red balls doubles. Find :1)p (red ball) 2) p (blue ball) 3) p (blue ball if of 5 extra red balls are actually added).
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Answer:
Step-by-step explanation:
⇒ Number of blue balls =15
⇒ Number of blue balss =x
⇒ Number of red balls =15−x
∴ Probability of taking a red ball =
15
15−x
Now, after 5 red balls are added,
⇒ Number of balls =15+5=20
⇒ Number of blue balls =x
⇒ Number of red balls =(15−x)+5=20−x
⇒ Probability of taking a red ball =
20
20−x
According to the question,
15
15−x
×2=
20
20−x
15
30−2x
=
20
20−x
600−40x=300−15x
300=25x
∴ x=
25
300
=12
∴ We have 12 blue balls and 3 red balls .
(i) P(redball)=
15
3
=
5
1
(ii) P(blueballs)=
15
12
(iii) P(blueballif5ballsareactuallyadded)=
15+5
12
=
20
12
=
5
3
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