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, $ $T H T T ,\, T T H H , \,T T H T ,\, T T T H , \,T T T T \}$
Two dice are thrown. The events $A,\, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$
State true or false $:$ (give reason for your answer)
Statement : $A$ and $B$ are mutually exclusive
The probability of $A, B, C$ solving a problem are $\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment ?
The probability of a sure event is
The chance of India winning toss is $3/4$. If it wins the toss, then its chance of victory is $4/5$ otherwise it is only $1/2$. Then chance of India's victory is