or QR. Similarly, corresponding to H, the second draw may be Q or R. Therefore, the outcomes may be HQ or HR. Lastly, corresponding to R, the second draw may be H or Q.
So, the outcomes may be RH or RQ. MATHEMATICS Thus, the sample space is S={QH, QR, HQ, HR, RH, RQ} The number of accidents along a busy highway during the year of observation can be either (for no accident ) or or , or some other positive integer. Thus, a sample space associated with this experiment is S= { , , ,...} Example A coin is tossed. If it shows head, we draw a ball from a bag consisting of blue and white balls; if it shows tail we throw a die.
Describe the sample space of this experiment. Solution Let us denote blue balls by B , B , B and the white balls by W , W , W , W . Then a sample space of the experiment is S = { HB , HB , HB , HW , HW , HW , HW , T1, T2, T3, T4, T5, T6}. Here HB i means head on the coin and ball B i is drawn, HW i means head on the coin and ball W i is drawn.
Similarly, T i means tail on the coin and the number i on the die. Example Consider the experiment in which a coin is tossed repeatedly until a head comes up. Describe the sample space. Solution In the experiment head may come up on the first toss, or the 2nd toss, or the 3rd toss and so on till head is obtained.Hence, the desired sample space is S= {H, TH, TTH, TTTH, TTTTH,...} EXERCISE .
In each of the following Exercises to , describe the sample space for the indicated experiment. . A coin is tossed three times. .
A die is thrown two times. . A coin is tossed four times. .