Describe the sample space for the indicated experiment: A coin is tossed four times.
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 =\{ HHHH , \,HHHT , \,HHTH $, $HHTT , \,HTHH , \,HTHT $, $ HTTH , \,HTTT ,$ $THHH,\, THHT, \,THTH, $ $T H T T ,\, T T H H , \,T T H T ,\, T T T H , \,T T T T \}$
A coin is tossed three times, consider the following events.
$A: $ ' No head appears ', $B:$ ' Exactly one head appears ' and $C:$ ' Atleast two heads appear '
Do they form a set of mutually exclusive and exhaustive events?
A fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is $12$.
A bag contains $9$ discs of which $4$ are red, $3$ are blue and $2$ are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be red.
There are $n$ letters and $n$ addressed envelopes. The probability that all the letters are not kept in the right envelope, is
For any event $A$