Complement of an Event

Q.

The two events $A$ and $B$ have probabilities $0.25$ and $0.50$ respectively.

The probability that both $A$ and $B$ occur simultaneously is $0.14$.

Then the probability that neither $A$ nor $B$ occurs is

1. $0.39$

2. $0.25$

3. $0.904$

4. None of these

Q. In a exam there are $30$ true/false questions. If a student guesses all the $30$ questions, then the probability that he/she gets atleast $15$ correct, is

1. $\frac{1}{2}+\frac{{}^{30}{C}_{15}}{2^{31}}$
2. $\frac{1}{2}$
3. $1-\frac{{}^{30}{C}_{15}}{2^{30}}$
4. $\frac{1}{2}+\frac{{}^{30}{C}_{15}}{2^{30}}$

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. An unbiased coin is tossed once. What is the complement of the following event X
X = {coin shows heads}

1. Coin shows either heads or tails
2. Coin shows heads and tails
3. Coin shows tails
4. None of the above

Q. Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2},\frac{3}{4},\frac{1}{4},\frac{1}{8}.$ Then, the probability that the problem is solved correctly by atleast one of them, is ?

1. $\frac{235}{256}$
2. $\frac{21}{256}$
3. $\frac{3}{256}$
4. $\frac{253}{256}$

Q. The smallest set A such that A ∪ {1, 2} = {1, 2, 3, 5, 9} is

लघुत्तम समुच्चय A कौनसा है जबकि A ∪ {1, 2} = {1, 2, 3, 5, 9} है

1. {2, 3, 5}
2. {3, 5, 9}
3. {1, 2, 5, 9}
4. {3, 5}

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. Let A and B be two events such that $P\left(\overline{A\cup B}\right)=\frac{1}{6},P(A\cap B)=\frac{1}{4}$ and $P\left(\overline{A}\right)=\frac{1}{4},where\overline{A}$ stands for the complement of the event A. Then, the events A and B are ?

1. Independent but not equally likely
2. Independent and equally likely
3. Mutually exclusive and independent
4. Equally likely but not independent

Q.

If p is the probability that a man aged x years will die in a year, find the probability that out of n men $A_1,A_2,...A_n$ each aged x years, $A_1$ will die in a year and will be the first to die.

1. $=\left(\frac{1}{n}\right)[1-p^n]$.

2. $=\left(\frac{1}{n}\right)[1-(1-p{)}^n]$.

3. $=\left(\frac{1}{n}\right)\left[\right(1-p{)}^n]$.

4. $=\left(\frac{1}{n}\right)[1-(2-p{)}^n]$.

Q. If $A$ and $B$ are two events such that $P\left(A\right)=\frac{3}{4}$ and $P\left(B\right)=\frac{5}{8}$, then

1. $P(A\cup B)\ge \frac{3}{4}$
2. $P(A^{\prime }\cup B)\ge \frac{1}{4}$
3. $\frac{3}{8}\le P(A\cup B)\le \frac{5}{8}$
4. $\frac{3}{8}\le P(A\cap B)\le \frac{5}{8}$

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 dice is rolled once. The following event is described.
A = {Getting 5 or 6}
Which of the following is the complement of A?

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