Question

A bag contains 5 black, 4 white balls and 3 red balls. If a ball is selected random wise, the probability that it is a black or red ball is
1) \[\dfrac{1}{3}\]
2) \[\dfrac{1}{4}\]
3) \[\dfrac{5}{{12}}\]
4) \[\dfrac{2}{3}\]

Answer 1

Hint: The given problem can be solved by finding favorable number of events and total number of elementary event and then we can use the formula for finding probability of an event and is given by \[{\text{probability of event = }}\dfrac{{{\text{favourable number of event}}}}{{{\text{total number of elementary event}}}}\] .

Complete step-by-step solution:
Given that a bag contains 5 black, 4 white balls and 3 red balls
 \[\therefore \] the total number of balls= \[5 + 4 + 3 = 12\]
The number of ways of choosing one ball from 12 balls \[ = 12{C_1}\]
\[\therefore \]total number of elementary events = \[ = 12{C_1} = 12\]
Now, out of five black balls, the number of ways of choosing one black ball \[ = 5{C_1} = 5\]
out of three red balls, the number of ways of choosing one red ball \[ = 3{C_1} = 3\]
\[\therefore \]favorable number of events \[ = 5 + 3 = 8\]
\[\therefore \] The probability of selecting a black or red ball is \[{\text{ = }}\dfrac{{{\text{favourable number of event}}}}{{{\text{total number of elementary event}}}}\]
\[\therefore \] The probability of selecting a black or red ball is\[ = \dfrac{8}{{12}} = \dfrac{2}{3}\]
Therefore, the correct answer is option 4) \[\dfrac{2}{3}\].

Note: Probability is the branch of mathematics concerning numerical descriptions of how likely an event (Any subset of the Sample Space S) is to occur, or how likely it is that a proposition is true.
In probability theory, an elementary event (also called an atomic event or sample point) is an event which contains only a single outcome in the sample space.(sample space The collection of all possible outcomes of a probability experiment forms a set that is known as the sample space).