Complement of an Event

Q. A fair die is tossed repeatedly until a $4$ or $6$ is obtained. If $x$ denotes the number of tosses required, then probability that $x\ge 3$ is $\frac{a}{b}$, where $a$ and $b$ are co-prime, then the value of $|a-b|$ is

Q. The probability of happening an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of happening neither A nor B is

1. None of these
2. 0.6
3. 0.2
4. 0.21

Q.

In a multiple choice question there are four alternative answers, of which one or more are correct. A candidate will get marks in the question only if he ticks all the correct answers. The candidate decides to tick answers at random. If he is allowed upto three chances to answer the question, find the probability that he will get marks in the question.___

Q.

A, B, C in order cut a pack of cards, replacing them after each cut, on the condition that the first who cuts a spade shall win a prize; find their respective chances.

1. $\frac{16}{37},\frac{12}{37},\frac{9}{37}$
2. $\frac{16}{21},\frac{4}{21},\frac{1}{21}$
3. $\frac{9}{37},\frac{12}{37},\frac{16}{37}$
4. $\frac{1}{21},\frac{4}{21},\frac{16}{21}$

Q. $\mathrm{If}\mathrm{an}\mathrm{experiment}\mathrm{is}\mathrm{conducted}\mathrm{by}\mathrm{throwing}a\mathrm{die}\mathrm{Event}A=\mathrm{any}\mathrm{prime}\mathrm{no}.\mathrm{Event}B=\mathrm{any}\mathrm{odd}\mathrm{no}\mathrm{Then}\mathrm{which}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{is}\mathrm{the}\mathrm{sample}\mathrm{space}\mathrm{of}\mathrm{an}\mathrm{event}A\cap \overline{B}?$

1. {3, 5}
2. {2}
3. {2, 3, 5}
4. {1, 2, 3, 4, 5, 6}

Q. $\mathrm{For}\mathrm{any}\mathrm{event}A,\mathrm{The}\mathrm{event}A\cup \overline{A}\mathrm{will}\mathrm{contain}\mathrm{all}\mathrm{the}\mathrm{elements}\mathrm{of}\mathrm{the}\mathrm{sample}\mathrm{space}$

1. True
2. False

Q.

If f is a polynomial function satisfying 2+f(x).f(y)=f(x)+f(y)+f(xy) for all x, y€ R and if f(2)=5 then find f(f(2)) .

(Answer given is 26)

(I just only need the solution and I know that there's no mistake in the answer given so please provide me with the correct solution with answer 26)

Q. If P(E) = 0 Then P(not E) is

1. -1
2. 1
3. 0
4. 1/2

Q. The probability that the least one of the events $A$ and $B$ occur is $0.6$, if $A$ and $B$ occur simultaneously with probability $0.2$, then $P\left(\overline{A}\right)+P\left(\overline{B}\right)$, where $\overline{A}$ and $\overline{B}$ are complements of $A$ and $B$ respectively is equal to

1. $0.4$
2. $0.8$
3. $1.2$
4. $1.4$
5. $Noneofthese$

Q. Four dice are rolled, then the probability that at least one digit on the dice must be repeated is

1. $\frac{1}{18}$
2. $\frac{5}{18}$
3. $\frac{1}{9}$
4. $\frac{13}{18}$