The word experiment means an operation which can produce some well-defined outcomes. There are two types of experiments (i) Deterministic experiments and (ii) Random or Probability experiments. In this exercise, we shall discuss the above experiments with suitable examples. Numerous solved examples are present before the exercise problems to provide a clear understanding among students. Students can self analyse their weaknesses and work on them to yield good results in the board exams.
Students can refer to RD Sharma Class 11 Maths Solutions and download the free PDF from the links given below.
RD Sharma Solutions for Class 11 Maths Exercise 33.1 Chapter 33 – Probability
Also, access other exercises of RD Sharma Solutions for Class 11 Maths Chapter 33 – Probability
Access answers to RD Sharma Solutions for Class 11 Maths Exercise 33.1 Chapter 33 – Probability
EXERCISE 33.1 PAGE NO: 33.6
1. A coin is tossed once. Write its sample space.
Solution:
Given: A coin is tossed once.
We know that the coin is tossed only once.
Then, there are two probabilities either Head (H) or Tail (T).
So,
S = {H, T}
∴ The sample space is {H, T}
2. If a coin is tossed two times, describe the sample space associated to this experiment.
Solution:
Given: If the Coin is tossed twice.
We know that two coins are tossed, which means two probabilities will occur at the same time.
So,
S = {HT, TH, HH, TT}
∴ Sample space is {HT, HH, TT, TH}
3. If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this experiment.
Solution:
Given: If a coin is tossed three times.
We know that the coins are tossed three times, and then the no. of samples is
23 = 8
So,
S = {HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
∴ The sample space is {HHH, TTT, HHT, HTH, THH, HTT, THT, TTH}
4. Write the sample space for the experiment of tossing a coin four times.
Solution:
Given: A coin is tossed four times.
We know that the coins are tossed four times, then the no. of samples
24 = 16
So,
S = {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH}
∴ The sample space is {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH}
5. Two dice are thrown. Describe the sample space of this experiment.
Solution:
Given: Two dice are thrown.
We know there are 6 faces on a die. Which contains (1, 2, 3, 4, 5, 6).
Here two dice are thrown, and then we have two faces of dice (one of each).
So, the total sample space will be 62 = 36
∴ The sample space is:
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 6), (5, 5), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
6. What is the total number of elementary events associated to the random experiment of throwing three dice together?
Solution:
Given: Three dice are rolled together.
We know that three dice are thrown together. And there are 6 faces on a die,
So, the total numbers of elementary events on throwing three dice are
6 × 6 × 6 = 216
∴ The total number of elementary events are 216
7. A coin is tossed and then a die is thrown. Describe the sample space for this experiment.
Solution:
Given: A coin is tossed, and a die is thrown.
We know that the coin is tossed, and the die is thrown.
So, when the coin is tossed there will be 2 events, either Head or Tail.
And, when the die is thrown, then there will be 6 faces (1, 2, 3, 4, 5, 6)
Then,
The total number of sample spaces together is 2 × 6 = 12
S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
∴ The sample space is {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
8. A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space for this experiment.
Solution:
Given: A coin is tossed, and the die is rolled.
We know that we have a coin and a die,
So, when the coin is tossed, there will be 2 events Head and tail,
According to the question, if it is Heads, then the die will be rolled out. Otherwise, it will not.
So, the sample spaces are:
S = {(T, (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)}
∴ The sample space is {T, (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)1}
9. A coin is tossed twice. If the second throw results in a tail, a die is thrown. Describe the sample space for this experiment.
Solution:
Given: A coin is tossed twice. If the second throw results in a tail, a die is thrown.
When a coin is tossed twice, then sample spaces for only one coin will be: {HH, TT, HT, TH}
Now, according to question, when we get Tail in the second throw, then a dice is thrown.
So, the total number of elementary events is 2 + (2×6) = 14
And sample space will be
S = {HH, TH, (HT, 1), (HT, 2), (HT, 3), (HT, 4), (HT, 5), (HT, 6), (TT, 1), (TT, 2), (TT, 3), (TT, 4), (TT, 5), (TT, 6)}
∴ The sample space is {HH, TH, (HT, 1), (HT, 2), (HT, 3), (HT, 4), (HT, 5), (HT, 6), (TT, 1), (TT, 2), (TT, 3), (TT, 4), (TT, 5), (TT, 6)}
10. An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the first toss, then a die is tossed once. Find the sample space.
Solution:
Given: A coin is tossed, and a die is rolled.
In the given experiment, the coin is tossed, and if the outcome is tail, then the die will be rolled.
The possible outcome for coin is 2 = {H, T}
And, the possible outcome for die is 6 = {1, 2, 3, 4, 5, 6}
If the outcome for the coin is tail, then sample space is S1= {(T, 1) (T, 2) (T, 3) (T, 4) (T, 5) (T, 6)}
If the outcome is head then the sample space is S2 = {(H, H) (H, T)}
So, the required outcome sample space is S = S1 ⋃ S2
S = {(T, 1) (T, 2) (T, 3) (T, 4) (T, 5) (T, 6) (H, H) (H, T)}
∴ The sample space for the given experiment is {(T, 1) (T, 2) (T, 3) (T, 4) (T, 5) (T, 6) (H, H) (H, T)}
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.
Solution:
Given: A coin is tossed, and there is a box which contains 2 red and 3 black balls.
When the coin is tossed, there are 2 outcomes {H, T}
According to the question, if tails turns up, the ball is drawn from a box.
So, sample for this experiment S1 = {(T, R1) (T, R2) (T, B1) (T, B2) (T, B3)}
Now, If heads turns up, then the die is rolled.
So, sample space for this experiment S2 = {(H, 1) (H, 2) (H, 3) (H, 4) (H, 5) (H, 6)}
The required sample space 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 elementary events associated with the given experiment.
12. A coin is tossed repeatedly until a tail comes up for the first time. Write the sample space for this experiment.
Solution:
Given: A coin is tossed repeatedly until tails 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…}
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