# Probability

## Class 11 NCERT

### NCERT

1   Describe the sample space for the indicated experiment: $A$ coin is tossed three times.

##### Solution :

$A$ coin has two faces: head $(H)$ and tail $(T).$$\\ When a coin is tossed three times, the total number of possible outcome is 2^ 3 = 8$$\\$ Thus, when a coin is tossed three times, the sample space is given by: $S = \{\text{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}\}$

2   Describe the sample space for the indicated experiment: $A$ die is thrown two times.

When a die is thrown, the possible outcomes are $1, 2, 3, 4, 5,$ or $6.$$\\ When a die is thrown two times, the sample is given by S = \{ ( x , y ) : x, y = 1, 2, 3, 4, 5, 6\} The number of elements in this sample space is 6 × 6 = 36, while the sample space is given by: S = \{ (1,1 ) , ( 1, 2 ) , ( 1,3 ) , ( 1, 4 ) , ( 1,6 ) , ( 2,1 ) , ( 2, 2 ) , ( 2,3 ) , (2, 4 ) , ( 2,5 ) , ( 2,6 ) , ( 3,1 ) ,\\ ( 3, 2 ) , ( 3,3 ) , ( 3,4 ) , ( 3,5 ) , ( 3,6 ) , ( 4,1 ) , ( 4, 2 ) , (4,3 ) , ( 4, 4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,1 ) , ( 5, 2 ) ,\\ ( 5,3 ) , ( 5, 4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,1 ) , ( 6, 2 ) , ( 6,3 ) , ( 6, 4 ) , ( 6,5 ) , ( 6,6 )\} 3 Describe the sample space for the indicated experiment: A coin is tossed four times. ##### Solution : When a coin is tossed once, there are two possible outcomes: head (H) and tail (T). When a coin is tossed four times, the total number of possible outcomes is 2^ 4 = 16$$\\$ Thus, when a coin is tossed four times, the sample space is given by: $S= \{\text{HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH,THTT, TTHH, TTHT, TTTH, TTTT}\}$

4   Describe the sample for the indicated experiment: $A$ coin is tossed and a die is thrown.