Question

A bag contains a red ball, a blue ball and a yellow ball , all the balls being of the same size. Krithika takes out a ball from the bag without looking into it . What is the probability that she takes out the
Yellow ball
Red ball
Blue ball
(i) $a)\dfrac{1}{2}b)\dfrac{1}{3}c)\dfrac{1}{2}$
(ii) $a)\dfrac{1}{3}b)\dfrac{1}{2}c)\dfrac{1}{3}$
(iii) $a)\dfrac{1}{3}b)\dfrac{1}{3}c)\dfrac{1}{3}$
(iv) $a)\dfrac{1}{2}b)\dfrac{1}{2}c)\dfrac{1}{2}$

Answer 1

Hint:
Since we are given that the bag contains a red ball , a blue ball and a yellow ball the total number of balls in the bag is 3 and when a ball is drawn in random the probability of drawing a specific colour ball is given by the ratio of number of balls of that colour to the total number of balls in the bag.

Complete step by step solution:
We are given that the bag contains a red ball , a yellow ball and a blue ball
Therefore the total number of balls in the bag is 3
$ \Rightarrow n\left( S \right) = 3$
Let A be the event of drawing a yellow ball
The number of yellow balls in the bag is 1
$ \Rightarrow n\left( A \right) = 1$
The probability of an event taking place is given by the formula
$
   \Rightarrow P\left( A \right) = \dfrac{{n\left( A \right)}}{{n\left( S \right)}} \\
   \Rightarrow P\left( A \right) = \dfrac{1}{3} \\
 $
 Hence the probability of drawing a yellow ball is $\dfrac{1}{3}$
Let B be the event of drawing a red ball
The number of red balls in the bag is 1
$ \Rightarrow n\left( B \right) = 1$
The probability of an event taking place is given by the formula
$
   \Rightarrow P\left( B \right) = \dfrac{{n\left( B \right)}}{{n\left( S \right)}} \\
   \Rightarrow P\left( B \right) = \dfrac{1}{3} \\
 $
 Hence the probability of drawing a red ball is $\dfrac{1}{3}$
Let C be the event of drawing a blue ball
The number of blue balls in the bag is 1
$ \Rightarrow n\left( C \right) = 1$
The probability of an event taking place is given by the formula
$
   \Rightarrow P\left( C \right) = \dfrac{{n\left( C \right)}}{{n\left( S \right)}} \\
   \Rightarrow P\left( C \right) = \dfrac{1}{3} \\
 $
 Hence the probability of drawing a blue ball is $\dfrac{1}{3}$

From this, the correct option is (iii).

Note:
Additional information :
1) A probability of 0 means that an event is impossible.
2) A probability of 1 means that an event is certain.
3) An event with a higher probability is more likely to occur.
4) Probabilities are always between 0 and 1.
5) The probabilities of our different outcomes must sum to 1.