Question

A bag contains 5red balls and some blue balls . if the probability of drawing a blue ball is double that of a red ball . determine the number of balls in the bag​

Answer 1

Answer:

• There are 15 balls in the bag.

Step-by-step explanation:

Given that:

• A bag contains 5 red balls and some blue balls.

Let us assume:

• A bag contains x blue balls.
• Total number balls in the bag = 5 + x

To Find:

The number of balls in the bag.

Formula used:

• P(E) = F/T

Where,

• P = Probability
• E = Events
• F = Favourable outcomes
• T = Total outcomes

Now we have,

• Total outcomes = 5 + x
• Favourable outcomes for blue ball = x
• Favourable outcomes for red ball = 5

Given that:

• The probability of drawing a blue ball is double that of a red ball.

P(drawing a blue ball) = 2 × P(drawing a red ball)

⇒ x/(5 + x) = 2 × 5/(5 + x)

Cancelling (5 + x) both sides.

⇒ x = 2 × 5

⇒ x = 10

∴ Total number balls in the bag = 5 + x = 5 + 10 = 15

Answer 2

Answer:

Given :-

A bag contain 5 red balls and some blue balls

To Find :-

Number of balls

Solution :-

Let the blue balls be y

And red balls be y + 5

Since the probability of red ball is double so,

$\sf \: \dfrac{y}{y + 5} = \dfrac{5 \times 2}{y + 5}$

$\sf \: \dfrac{y}{y + 5} = \dfrac{10}{y + 5}$

Cancelling y + 5

$\sf \: y = 10$

Number of balls

$\sf\red{y + 5}$

$\sf \: 10 + 5$

$\sf \pink{{15 \: balls}}$