1. A coin is tossed three times.
Solution:-
Since either coin can turn up Head (H) or Tail (T), the possible outcomes may be
When 1 coin is tossed once the sample space = 2
Then,
The coin is tossed 3 times the sample space = 23 = 8
Thus, the sample space is S = {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}
2. A die is thrown two times.
Solution:-
Let us assume that 1, 2, 3, 4, 5 and 6 are the possible outcomes when the die is thrown.
Then, the total number of the sample space = (6 × 6)
= 36
Thus, 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),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
3. A coin is tossed four times.
Solution:-
Since either coin can turn up Head (H) or Tail (T), the possible outcomes are
When 1 coin is tossed once the sample space = 2
Then,
The coin is tossed 3 times the sample space = 24 = 16
Thus, the sample space is S = {HHHH, THHH, HTHH, HHTH, HHHT, TTTT, HTTT, THTT, TTHT, TTTH, TTHH, HHTT, THTH, HTHT, THHT, HTTH}
4. A coin is tossed, and a die is thrown.
Solution:-
A coin can turn up either Head (H) or Tail (T), and this is the possible outcome.
Let us assume that 1, 2, 3, 4, 5 and 6 are the possible numbers that come when the die is thrown.
Then, total number of space = (2 × 6) = 12
Thus, the sample space is,
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)}
5. A coin is tossed, and then a die is rolled only in case a head is shown on the coin.
Solution:-
Since either coin can turn up Head (H) or Tail (T), these are the possible outcomes.
Let us assume that 1, 2, 3, 4, 5 and 6 are the possible numbers that come when the die is thrown.
When the head is encountered,
Then, number of space = (1 × 6) = 6
Sample Space SH= {H1, H2, H3, H4, H5, H6}
Now, the tail is encountered, Sample space ST= {T}
Therefore the total sample space S = {H1, H2, H3, H4, H5, H6, T}
6. 2 boys and 2 girls are in Room X, and 1 boy and 3 girls are in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.
Solution:-
From the question, it is given that
2 boys and 2 girls are in Room X
1 boy and 3 girls in Room Y
Let us assume b1, b2 and g1, g2 be 2 boys and 2 girls in Room X.
And also, assume b3 and g3, g4, g5 be 1 boy and 3 girls in Room Y.
The problem is solved by dividing it into two cases.
Case 1: Room X is selected
Sample Space Sx = {(X,b1),(X,b2),(X,g1),(X,g2)}
Case 2: Room Y is selected
Sample Space Sy ={(Y,b3),(Y,g3),(Y,g4),(Y,g5)}
The overall sample space
S={(X,b1),(X,b2),(X,g1),(X,g2),(Y,b3),(Y,g3),(Y,g4),(Y,g5)}
7. One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.
Solution:-
Let us assume that 1, 2, 3, 4, 5 and 6 are the possible numbers that come when the die is thrown.
And also, assume die of red colour be ‘R’, die of white colour be ‘W’, die of blue colour be ‘B’.
So, the total number of sample space = (6 × 3) = 18
The sample space of the event is
S={(R,1),(R,2),(R,3),(R,4),(R,5),(R,6),(W,1),(W,2),(W,3),(W,4),(W,5),(W,6) (B,1),(B,2),(B,3),(B,4),(B,5),(B,6)}