Question

The probability of selecting a redball at random from a jar that contains only red, Blue orange balls is 1/4. Probability of selecting a blue Ball from the same jar is 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar?

Answer 1

Question

The probability of selecting a redball at random from a jar that contains only red, blue and orange balls and of red ball is 1/4. Probability of selecting a blue ball from the same jar is 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar?

Solution

Let us assume that there are total x number of balls.

Given that, probability of selecting a red ball at random from a jar is 1/4.

⇒ P(red ball) = 1/4

Also, the probability of selecting a blue ball from the same jar is 1/3.

⇒ P(blue ball) = 1/3

There are total 10 orange balls in the jar.

⇒ P(orange ball) = 10/x

Now,

P(red ball) + P(blue ball) + P(orange ball) = 1

Substitute the known values,

⇒ 1/4 + 1/3 + 10/x = 1

⇒ 10/x = 1 - (1/4 + 1/3)

⇒ 10/x = 1 - [(4 + 3)/12]

⇒ 10/x = 1 - 7/12

⇒ 10/x = (12 - 7)/12

⇒ 10/x = 5/12

Cross-multiply them

⇒ 5x = 12 × 10

⇒ 5x = 120

⇒ x = 120/5

⇒ x = 24

Therefore,

Total number of balls in the jar = 24

Answer 2

Given :-

• probability of selecting a red ball at random from a jar is 1/4.
• Probability of selecting a blue Ball from the same jar is 1/3.
• Total orange balls in Jar = 10 .

To Find :-

• find the total number of balls in the jar ?

Solution :-

Let us Assume That, Total number of balls in the jar is X.

A/q,

→ Probability of Number of Red Balls in The = (1/4)

So,

→ (Total Number of Events / Total Number of Outcomes) = (1/4)

→ (Total Number of Events / X) = 1/4

→ Total Number of Events = (x/4) .

Or,

→ Total Red Balls = (x/4). ------------------ Equation (1)

_____________________

Similarly,

→ Probability of Number of Blue Balls in The = (1/3)

So,

→ (Total Number of Events / Total Number of Outcomes) = (1/4)

→ (Total Number of Events / X) = 1/3

→ Total Number of Events = (x/3) .

Or,

→ Total Blue Balls = (x/3). ------------------ Equation (2)

_____________________

And, Given That :-

→ Total Number of Orange Balls Are = 10.------ Equation (3).

____________________

Adding Equation (1) , (2) & (3), we get, Total Number of Balls in The Jar.

So,

→ (x/4) + (x/3) + 10 = x

Taking LCM,

→ (3x + 4x + 120) /12 = x

Cross - Multiply,

→ 7x + 120 = 12x

→ 12x - 7x = 120

→ 5x = 120

Dividing Both Sides by 5,

→ x = 24. (Ans).

Hence, The total number of balls in the jar are 24.