Math, asked by mayamalhotra4642, 5 hours ago

There are 21 balls in a bag. Some red and some yellow. If a ball is chosen at random from the bag, the probability of choosing a red is 2/3. How many yellow balls are in the bag?

Answers

Answered by tennetiraj86
3

Step-by-step explanation:

Given :-

There are 21 balls in a bag. Some red and some yellow. If a ball is chosen at random from the bag, the probability of choosing a red is 2/3.

To find :-

How many yellow balls are in the bag?

Solution :-

Given that :

Total number of balls in a bag = 21

Total number of all possible outcomes = 21

Let the number of yellow balls be X

Then,

The number of red balls = 21-X

We know that

Probability of an event =Number of favourable outcomes/ Total number of all possible outcomes

Probability of getting red ball

Number of favourable outcomes to red ball/ Total number of all possible outcomes

= (21-X)/21

According to the given problem

Probability of getting a red ball = 2/3

=> (21-X)/21 = 2/3

On applying cross multiplication then

=> 3(21-X) = 21×2

=> 63-3X = 42

=> -3X = 42-63

=> -3X = -21

=> 3X = 21

=> X = 21/3

=> X = 7

Yellow balls =7

Answer:-

The number of yellow balls in the bag is 7

Check :-

Yellow balls = 7

Red balls = 21-7 = 14

Probability of getting a red ball

=>Number of favourable outcomes to red ball/ Total number of all possible outcomes

=> 14/21

=> (2×7)/(3×7)

=> 2/3

Verified the given relations in the given problem

Used formulae:-

Probability of an event =Number of favourable outcomes/ Total number of all possible outcomes

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