JEE Mathematics / Probability / Understanding Sample Space of a Random experiment involving tossing of coins and rolling of dice with Questions and Answers

1. 6Physics Helpline
L K Satapathy
Probability Theory 2

2. Physics Helpline
L K Satapathy
Q : A coin is tossed. If a head occurs, then it is tossed again. If a tail
occurs in the first toss then a die is rolled once. Find the sample space.
Ans: When the coin is tossed once, the outcomes are head (H) or tail (T)
(i) When H occurs in the 1st toss , it is tossed again.
The possible outcomes of the 2nd toss are H or T
 When H occurs in the 1st toss , we get HH or HT
(ii) When T occurs in the 1st toss , a die is rolled once
The possible outcomes of the die are 1 , 2 , 3 , 4 , 5 or 6
 When T occurs in the 1st toss , we get T1 , T2 , T3 , T4 , T5 or T6
 S = { HH , HT , T1 , T2 , T3 , T4 , T5 , T6 }
Probability Theory 2

3. Physics Helpline
L K Satapathy
Tabulation Method
 S = { HH , HT , T1 , T2 , T3 , T4 , T5 , T6 }
If the 1st toss of coin shows head (H)
We toss it again which gives H or T
If the 1st toss of coin shows tail (T)
We roll a die which gives
1 , 2 , 3 , 4 , 5 or 6
1st Toss 2nd Toss Rolling of die
H
H
H
T
―
―
T
T
T
T
T
T
1
2
3
4
5
6
―
―
―
―
―
―
Probability Theory 2

4. Physics Helpline
L K Satapathy
Q : A coin is tossed. If the outcome is a head , then a die is rolled . If the
die shows an even number, then it is rolled again. Find the sample
space.
When H occurs, we roll a die whose outcomes are 1 , 2 , 3 , 4 , 5 or 6
 When H occurs in the toss , we get H1 , H2 , H3 , H4 , H5 or H6
When T occurs, we stop
For an odd number on the die, we stop  H1 , H3 , H5
For an even number on die (H2 , H4 , H6) , we roll it again
 S = { T , H1 , H3 , H5 , H21 , H22 , H23 , H24 , H25 , H26 , H41, H42 ,
H43 , H44 , H45 , H46 , H61 , H62 , H63 , H64 , H65 , H66 }
Ans: When the coin is tossed once, the outcomes are head (H) or tail (T)
Probability Theory 2

5. Physics Helpline
L K Satapathy
―
Toss 1st Roll 2nd Roll
T ―
H 1
2
3
4
5
6
H
H
H
H
H
2
2
2
2
2
2
Tabulation Method
When T occurs on toss of coin , we stop
When H occurs on toss of coin , we roll a die
When odd number occurs on it , we stop
When H occurs on toss of coin and even
number (2) occurs on die , we roll it again
whose outcomes are 1, 2, 3, 4, 5 or 6
H ―
H
H
1
3
5
―
―
Probability Theory 2

6. Physics Helpline
L K Satapathy
H 1
2
3
4
5
6
H
H
H
H
H
4
4
4
4
4
4
H 1
2
3
4
5
6
H
H
H
H
H
6
6
6
6
6
6
 S = { T , H1 , H3 , H5 , H21 , H22 , H23 , H24 , H25 , H26 , H41, H42 ,
H43 , H44 , H45 , H46 , H61 , H62 , H63 , H64 , H65 , H66 }
When H occurs on toss of coin and even
number (4) occurs on die , we roll it again
whose outcomes are 1, 2, 3, 4, 5 or 6
When H occurs on toss of coin and even
number (6) occurs on die , we roll it again
whose outcomes are 1, 2, 3, 4, 5 or 6
Probability Theory 2

7. Physics Helpline
L K Satapathy
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