There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 7 over 9 . There are 28 red marbles in the bag and each is equally likely to be chosen. Work out how many marbles in total there must be.
Answers
Given :-
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is 7/9 .
There are 28 red marbles in the bag and each is equally likely to be chosen.
To find :-
Total number of all marbles in the bag
Solution :-
Let the number of green marbles be X
The number of favourable outcomes to green marble = X
The number of red marbles = 28
The number of favourable outcomes to red marble = 28
Total number of marbles in the bag
= 28+X
Total number of all possible outcomes
= 28+X
We know that
Probability of an event E is P(E)
= Number of favourable outcomes/Total number of a possible outcomes
Probability of getting a red marble P(R)
= 28/(28+X)
According to the given problem
Probability of getting a red marble = 7/9
Therefore, 28/(28+X) = 7/9
On applying cross multiplication then
=> (28+X)×7 = 28×9
=> 196 + 7X = 252
=> 7X = 252-196
=> 7X = 56
=> X = 56/7
=> X = 8
Therefore, The number of green marbles = 8
The number of all marbles in the bag
= Green marbles + Red marbles
= 8+28
= 36
Answer :-
The total number of all marbles in the bag is 36
Check :-
Number of green marbles = 8
Number of red marbles = 28
Total number of all marbles = 36
Probability of getting a red marble
=> P(R) = 28/36
=> P(R) = (7×4)/(9×4)
=> P(R) = 7/9
Verified the given relations in the given problem.
Used formulae:-
→ Probability of an event E is P(E)= Number of favourable outcomes/Total number of a possible outcomes
Answer:
- Refer the αttαchment...!
