Question

A bag contains \[4\] white, \[5\] black and \[6\] red balls. If a ball is drawn at random, then what is the probability that the drawn ball is white or red.
A. \[\dfrac{4}{{15}}\]
B. \[\dfrac{1}{2}\]
C. \[\dfrac{2}{5}\]
D. \[\dfrac{2}{3}\]

Answer 1

Hint:In this question we have to find the probability of drawing a ball which is white or red. We will find the total number of balls, and the total number of drawing white or red balls drawn. We will then divide the number of white or red balls by the total number of balls to get the desired result.

Complete step by step answer:
The given question is based on the probability of drawing a ball out of a ball of different colours. Consider the given question,
Total number of white ball \[ = \]\[4\]
Total number of red ball \[ = \]\[6\]
Total number of black ball \[ = \]\[5\]
Total number of balls \[ = \]\[4 + 5 + 6 = 15\]
Let E be an event of drawing a white or red ball.
Total number of ball ( white + red ) \[ = \]\[4 + 6 = 10\]
Then probability of drawing a white or red ball is given by
\[P(E) = \dfrac{{{\text{total no of ball( white + red )}}}}{{{\text{total no of balls }}}}\]
Putting the values we have,
\[P(E) = \dfrac{{10}}{{15}}\]
On simplifying by dividing numerator and denominator by 5 we get,
\[\therefore P(E) = \dfrac{2}{3}\]
Hence the probability of drawing a white or red ball is \[\dfrac{2}{3}\].

Hence, option D is correct.

Note:Probability is defined as the number of favourable outcomes divided by the total number of outcomes i.e,
\[P(E) = \dfrac{{{\text{Number of favourable outcome}}}}{{{\text{total number of outcome}}}}\]
The value of probability always lies between \[0\] and \[1\]. Probability of an impossible event is zero and of a sure event is one. For example, the probability of getting \[7\] when a dice is rolled is zero, since \[7\] is not an outcome when dice is rolled.