Question

a box contains 15 balls out of which x are black and remaing are red . If probability of drawing a black ball is twice the probability of drawing red, find numbers of balls of each type in the box​

Answer 1

Answer:

No Of Balls = 15

No Of Blue Balls = x

No Of Red Balls = 15 - x

Probability of taking a red ball is; P(E) = 15 - x

15

After 5 red balls are added,

No of balls = 15 + 5 = 20

No of blue balls = x

No of Red Balls = (15 - x) + 5 = 20 - x

Probability of taking a red ball is; P(E) = 20 - x

20

According to your question, 15 - x x 2 = 20 - x

15 20

30 - 2x = 20 - x

15 20

600 - 40 x = 300 - 15 x

300 = 25 x

x = 12 [ Blue Balls ]

Answer 2

Correct Question :---- A box contains 15 balls of which x are black and remaining are red. if the number of red balls are increased by 5 the probability of red ball doubles, find numbers of balls of each type in the box ... ?

Probability :--- Probability is a numerical description of how likely an event is to occur or how likely it is that a proposition is true.

Solution :----

Case 1 says that :---

→ Total balls = 15

→ Let Number of black balls are = x

→ Than Number of Red balls = (15-x)

→ So, Probability of Balls being red = No. of Red balls / Total Number of balls = (15-x)/15

______________________________

Now,

Case 2 says That :---

5 red balls are added now ...

→ Total balls now = 15 + 5 = 20 balls

→ As black balls are same = x

→ Red balls = (15-x) + 5 = (20-x)

→ Probability of Being one red ball now = (20-x)/20

______________________________

According To Question Now,,

→ (20-x)/20 = 2 [ (15-x)/15 ]

→ 15(20-x) = 40(15-x)

→ 300 - 15x = 600 - 40x

→ -15x + 40x = 600-300

→ 25x = 300

Dividing both sides by 25

→ x = 12 balls = Number of Black balls ...

so, Number of red balls = 15 - 12 = 3 red balls..

__________________________

Hence, we can say that, there were 3 red balls and 12 black balls in the box....