Complement of an Event

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

Q.

Show that $A\cap B=A\cap C$ need not imply $B=C.$

Q.

Given $P\left(A\right)=\frac{3}{5},P\left(B\right)=\frac{1}{5}$ Find P(A or B), If A and B are mutually exclusive events.

Q. 27. The probability that an archer hits the target when it is windy is equal to 1/5, when it is not windy his probability of hitting the target is 2/5. On any shot the probability of gust of wind is 2/5. the probability that there is gust of wind on the occasion when he hits the target is equal to ?

Q.

If 2/7 is the probability of an event, then the probability of the event not A is:

1. 

2. 

3. 

4. 

Q. A pair of unbiased dice are rolled together till a sum of either 5 or 7 is obtained. Probability that 5 comes before 7 is

1. $\frac{1}{5}$
2. $\frac{2}{5}$
3. $\frac{3}{5}$
4. $\frac{4}{5}$

Q. 28. A and B are equally good tennis players. Which of the following two events is more probable? (i) A beats B exactly in 3 games out of 4.(ii) A beats B exactly in 5 games out of 8.

Q.

A ship is fitted with three engines $E_1,E_{2}and{E}_3$. The engines function independently of each other with respective probabilities $\frac{1}{2},\frac{1}{4}and\frac{1}{4}$. For the ship to be operational, at least two of its engines must function. Let X denote the event that the ship is operational and let $X_1,X_{2}and{X}_3$ denote, respectively the events that the engines $E_1,E_{2}and{E}_3$ are functioning.
Which of the following is/are true?

1. $P\left(X_1^C|X\right)=\frac{3}{16}$

2. P (Exactly two engines of the ship are functioning | X) $=\frac{7}{8}$

3. $P\left(X|X_2\right)=\frac{5}{16}$

4. $P\left(X|X_1\right)=\frac{7}{16}$

Q.

A die is rolled and the outcomes are observed. Event A is an even number turns up and event B is a prime number turns up. Match the events on left with the outcomes on right.

$\begin{array}{cc}1.\text{Event A or B}& P.\{4,6\}\\ 2.\text{Event A and B}& Q.\left\{2\right\}\\ 3.\text{Event A but not B}& R.\{2,3,4,5,6,\}\\ 4.\text{Complementary event of B}& S.\{1,4,6\}\end{array}$

1. 1 - R, 2 - Q, 3 - S, 4 - P

2. 1 - Q, 2 - R, 3 - P, 4 - S

3. 1 - R, 2 - Q, 3 - P, 4 - S

4. 1 - R, 2 - S, 3 - Q, 4 - P

Q. 29. The probability of a bomb hitting a bridge is 0.5 and 2 direct hits are needed to destroy it.The least number of bombs required so that the prob of bridge being destroyed is greater than 0.9 is

Q. $2$ boys and $2$ girls are in Room $X$ and $1$ boy and $3$ girls in Room $Y$ Specify the sample space for the experiment in which a room is selected and then a person

Q. 6. A and B are two independent events such that P(A union B) is equal to 0.8 and P(A) is equal to 0.3.The P(B) is

Q. Find the derivative of $x^{-3}(5+3x)$

Q.

An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?

1. 0.6976

2. 0.6776

3. 0.5976

4. 0.6276

Q. If $E$ and $F$ are events such that $P\left(E\right)=$ $\frac{1}{4}$, $P\left(F\right)=$ $\frac{1}{2}$ and $P\left(EandF\right)=$ $\frac{1}{8}$ find: (i) P(E or F) (ii) P(not E and not F)

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.

The range of the first five whole numbers is_____.

Q. If A and B are any two events, then the probability that exactly one of them occur, is

1. $P(A\cap \overline{B})+P(\overline{A}\cap B)$
2. $P(A\cup \overline{B})+P(\overline{A}\cup B)$
3. $P\left(A\right)+P\left(B\right)-P(A\cap B)$
4. $P\left(A\right)+P\left(B\right)+2P(A\cap B)$

Q. A and B are 2 sets such that n(A) = 12 and n(B) = 18, then n(A ∪ B) can have its maximum value as

2 समुच्चय A तथा B हैं जबकि n(A) = 12 तथा n(B) = 18 है, तब n(A ∪ B) का अधिकतम मान हो सकता है

1. 25
2. 12
3. 18
4. 30

Q. 12 identical balls are to be placed in 3 boxes. Probability that one of the box contains exactly 3 balls

Q. 67. 2 friends jhon and daisy , both have one dice each.both of them toss the dice.if the highest number among the two dice is less than 5 , jhon wins otherwise daisy wins.who has the highest chance of winning?

Q. 11.2 friends jhon and daisy , both have one dice each.both of them toss the dice.if the highest number among the two dice is less than 5 , jhon wins otherwise daisy wins.who has the highest chance of winning?

Q. If A and B are two events associated with a random experiment such that
P(A) = 0.3, P (B) = 0.4 and P (A ∪ B) = 0.5, find P (A ∩ B).