Question

There are 30 blue balls and x red balls in a bag. A ball is drawn at random from the bag. Write down, in terms of x an expression for the probability that the ball drawn is red.

Answer 1

Hint:- We have to find the total numbers of balls in the bag so we can directly use the formula of probability of favourable outcome = \[\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total numbers of outcomes}}}}\] to find the probability of the getting a red ball.

Complete step-by-step answer:
As we know that the number of red balls in the bag is x.
And the number of blue balls in the box is 30.
So, the total number of balls in the box will be the sum of red and blue balls = x + 30
Now as we know the formula of probability that probability of getting a ball of particular type form bag = \[\dfrac{{{\text{Number of balls of that type in the bag}}}}{{{\text{Total numbers of balls in the bag}}}}\]
So, if the ball is drawn from the bag.
Then, the probability that the ball drawn is red = \[\dfrac{{{\text{Number of red balls in the bag}}}}{{{\text{Total numbers of balls in the bag}}}} = \dfrac{x}{{x + 30}}\]
Hence, the probability that the ball drawn is red = \[\dfrac{x}{{x + 30}}\]

Note:- Whenever we come up with this type of problem then there is only one easiest method to solve the problem and that is we can directly apply probability formula to get the probability of getting a particular type of ball, So, for that we had to first find number of balls of that particular type and the total number of balls (all types) in the bag then probability = \[\dfrac{{{\text{Number of balls of that type }}\left( {{\text{here red}}} \right)}}{{{\text{Total numbers of balls }}\left( {{\text{Red + blue}}} \right)}}\]. This will be the efficient way to find the solution of the problem.