Consider the experiment in which a coin is tossed repeatedly until a head comes up. Describe the sample space.
In the experiment head may come up on the first toss, or the $2^{ nd}$ toss, or the $3^{rd}$ toss and so on till head is obtained. Hence, the desired sample space is
$S =\{ H , \,TH , \,TTH , \,TTTH ,\, TTTTH,$ ........ $\}$
A number is chosen from first $100$ natural numbers. The probability that the number is even or divisible by $5$, is
Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :
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
For independent events ${A_1},\,{A_2},\,..........,{A_n},$ $P({A_i}) = \frac{1}{{i + 1}},$ $i = 1,\,\,2,\,......,\,\,n.$ Then the probability that none of the event will occur, is
One card is drawn from a well shuffled deck of $52$ cards. If each outcome is equally likely, calculate the probability that the card will be not a black card.