RD Chapter 33 Probability Ex 33.1 Solutions
Question - 11 : - A coin is tossed. If it shows tail, we draw a ball from a box which contains 2 red 3 black balls; it shows head, we throw a die. Find the sample space of this experiment.
Answer - 11 : -
Given: A coin istossed and there is box which contains 2 red and 3 black balls.
When coin is tossed,there are 2 outcomes {H, T}
According to question,if tail turned up, the ball is drawn from a box.
So, sample for thisexperiment S1 = {(T, R1) (T, R2) (T, B1)(T, B2) (T, B3)}
Now, If Head is turnedup, and then die is rolled.
So, sample space forthis experiment S2 = {(H, 1) (H, 2) (H, 3) (H, 4) (H, 5) (H,6)}
The required samplespace will be S = S1 ⋃ S2
So,
S = {(T, R1),(T, R2), (T, B1), (T, B2), (T, B3),(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)}
∴ S is the elementaryevents associated with the given experiment.
Question - 12 : - A coin is tossed repeatedly until a tail comes up for the first time. Write the sample space for this experiment.
Answer - 12 : -
Given: A coin is tossed repeatedly until comes up for the first time.
In the given Experiment, a coin is tossed and if the outcome is tail the experiment is over.
And, if the outcome is Head then the coin is tossed again.
In the second toss also if the outcome is tail then experiment is over, otherwise coin is tossed again.
This process continues indefinitely
So, the sample space for this experiment is
S = {T, HT, HHT, HHHT, HHHHT…}
∴ The sample space for the given experiment is {T, HT, HHT, HHHT, HHHHT…}