Question

In a bag there are \[3\]balls; one black, one red and one green. Two balls are drawn one after another with replacement. State sample space and n(S).

Answer 1

Hint: In this type of problem, we should remember the concept of sample space in probability. Then we create the sample space for a given random variable. Now apply the given condition for these given random variables and again create a new sample space. This new sample space is our sample space after the replacement of the variable.

Complete step-by-step answer:
Sample space ={\[1\]Red ball, \[1\] Black ball, \[1\] Green ball}
And n(S) = \[3\]
Since, Bag has \[3\] balls. One black, one red and one green.
As Two balls are drawn one after another with replacement, i. e. one ball taken out and drop again in the bag, then another ball is taken out from the bag.
Since for both the conditions sample space remains the same.
Sample space is the range of values of a random variable. So, in the given condition.
$\Rightarrow$ Sample space = {\[1\]Red ball, \[1\]Black ball, \[1\]Green ball}
Hence, n(S) = \[3\]

Note: In the given question, we have three different balls with colour black, red and green. According to the condition in the given question we drew two balls from the given total three balls. Here, after one ball drawn from the bag replacement occurs into the bag.
So, we see into the number of balls into the bag there is no change into the number of balls in the bag. So, sample space is not changed.