# A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is: ${\text{(i)}}$ red ${\text{(ii)}}$ black or white ${\text{(iii)}}$ not black

Last updated date: 21st Mar 2023

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Answer

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Hint- Here, we will be using the general formula for probability of occurrence of an event.

Given, the bag contains 5 black, 7 red and 3 white balls.

Therefore, total number of balls in the bag\[ = 5 + 7 + 3 = 15\]

As we know that the general formula for probability is given by

\[{\text{Probability of occurrence of an favourable event = }}\dfrac{{{\text{Total number of favourable outcomes}}}}{{{\text{Total number of possible outcomes}}}}\]

\[{\text{(i)}}\] Here, we have to find the probability of drawing a red ball out of the bag. So, the favourable event here is drawing a red ball.

Total number of red balls in the bag\[ = 7\]

\[\therefore {\text{Probability of drawing a red ball = }}\dfrac{{{\text{Total number of red balls in the bag}}}}{{{\text{Total number of balls in the bag}}}} = \dfrac{7}{{15}}\].

${\text{(ii)}}$ Here, we have to find the probability of drawing a black or white ball out of the bag. So, the favourable event here is drawing a black or white ball.

Number of black balls in the bag\[ = 5\]

Number of white balls in the bag\[ = 3\]

Total number of black or white balls in the bag is equal to the sum of the number of black balls and white balls in the bag.

i.e., Total number of black or white balls in the bag\[ = 5 + 3 = 8\]

\[\therefore {\text{Probability of drawing a black or white ball = }}\dfrac{{{\text{Total number of black or white balls}}}}{{{\text{Total number of balls in the bag}}}} = \dfrac{8}{{15}}\].

\[{\text{(iii)}}\] Here, we have to find the probability of not drawing a black ball out of the bag which means probability of drawing a red or white ball out of the bag. So, the favourable event is drawing a red or white ball.

Number of red balls in the bag\[ = 7\]

Number of white balls in the bag\[ = 3\]

Total number of red and white balls in the bag\[ = 7 + 3 = 10\]

Therefore, Probability of not drawing a black ball$ = $Probability of drawing a red or white ball\[ = \dfrac{{{\text{Total number of red and white balls}}}}{{{\text{Total number of balls in the bag}}}} = \dfrac{{10}}{{15}} = \dfrac{2}{3}\].

Note- These types of problems can be easily solved by using the general formula for probability which includes the consideration of occurrence of an favourable event which is asked in the problem itself.

Given, the bag contains 5 black, 7 red and 3 white balls.

Therefore, total number of balls in the bag\[ = 5 + 7 + 3 = 15\]

As we know that the general formula for probability is given by

\[{\text{Probability of occurrence of an favourable event = }}\dfrac{{{\text{Total number of favourable outcomes}}}}{{{\text{Total number of possible outcomes}}}}\]

\[{\text{(i)}}\] Here, we have to find the probability of drawing a red ball out of the bag. So, the favourable event here is drawing a red ball.

Total number of red balls in the bag\[ = 7\]

\[\therefore {\text{Probability of drawing a red ball = }}\dfrac{{{\text{Total number of red balls in the bag}}}}{{{\text{Total number of balls in the bag}}}} = \dfrac{7}{{15}}\].

${\text{(ii)}}$ Here, we have to find the probability of drawing a black or white ball out of the bag. So, the favourable event here is drawing a black or white ball.

Number of black balls in the bag\[ = 5\]

Number of white balls in the bag\[ = 3\]

Total number of black or white balls in the bag is equal to the sum of the number of black balls and white balls in the bag.

i.e., Total number of black or white balls in the bag\[ = 5 + 3 = 8\]

\[\therefore {\text{Probability of drawing a black or white ball = }}\dfrac{{{\text{Total number of black or white balls}}}}{{{\text{Total number of balls in the bag}}}} = \dfrac{8}{{15}}\].

\[{\text{(iii)}}\] Here, we have to find the probability of not drawing a black ball out of the bag which means probability of drawing a red or white ball out of the bag. So, the favourable event is drawing a red or white ball.

Number of red balls in the bag\[ = 7\]

Number of white balls in the bag\[ = 3\]

Total number of red and white balls in the bag\[ = 7 + 3 = 10\]

Therefore, Probability of not drawing a black ball$ = $Probability of drawing a red or white ball\[ = \dfrac{{{\text{Total number of red and white balls}}}}{{{\text{Total number of balls in the bag}}}} = \dfrac{{10}}{{15}} = \dfrac{2}{3}\].

Note- These types of problems can be easily solved by using the general formula for probability which includes the consideration of occurrence of an favourable event which is asked in the problem itself.

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