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
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