Random Experiment

Q.

An experiment is called random experiment if

1. It has more than one possible outcome

2. We are able to predict the outcome in advance

3. It is not possible to predict the outcome in advance

4. It has only one possible outcome

Q. A box $B_1$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_2$ contains 2 white balls, 3 red balls and 4 black balls. A third box $B_3$ contains 3 white ball, 4 red balls and 5 black balls. If one ball is drawn from each of the boxes $B_1,B_2$ and $B_3$, the probability that all three drawn balls are of the same colour is

1. $\frac{82}{648}$
2. $\frac{90}{648}$
3. $\frac{558}{648}$
4. $\frac{566}{648}$

Q. The event of getting a number greater than 6 on rolling a single die is called a random experiment.

1. False
2. True

Q. A box $B_1$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_2$ contains 2 white balls, 3 red balls and 4 black balls. A third box $B_3$ contains 3 white ball, 4 red balls and 5 black balls. If one ball is drawn from each of the boxes $B_1,B_2$ and $B_3$, the probability that all three drawn balls are of the same colour is

1. $\frac{82}{648}$
2. $\frac{90}{648}$
3. $\frac{558}{648}$
4. $\frac{566}{648}$

Q. $\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{Let}n\text{be a number chosen randomly from}& & \\ & \text{the set of first}100\text{natural numbers. Then}& & \\ & \text{the probability that the value of}(1+i{)}^n& & \\ & \text{is real, is}& \text{(P)}& 2\\ \text{(B)}& \text{If the coefficient of}{x}^{13}\text{in the expansion of}& & \\ & (1-x{)}^5(1+x+x^2+x^3{)}^4\text{is}k\text{, then the}& & \\ & \text{value of}\frac{k}{4}\text{is}& \text{(Q)}& 0.35\\ \text{(C)}& \text{In an examination of}9\text{papers, a candidate}& & \\ & \text{has to pass in more papers than (s)he fails in}& & \\ & \text{order to be successful. If the number of}& & \\ & \text{ways in which (s)he can be unsuccessful is}{2}^m,& & \\ & \text{then the value of}\frac{m}{4}\text{is}& \text{(R)}& 0.55\\ \text{(D)}& A,B,C\text{are three events such that}& & \\ & P\left(A\right)=0.6,P\left(B\right)=0.4,P\left(C\right)=0.5,& & \\ & P(A\cup B)=0.8,P(A\cap C)=0.3\text{and}& & \\ & P(A\cap B\cap C)=0.2\text{. If}P(A\cup B\cup C)\ge 0.85& & \\ & \text{and}P(B\cap C)\text{lies in the interval}[0.2,b]\text{,}& & \\ & \text{then the value of}b\text{is}& \text{(S)}& 1\\ & & \text{(T)}& 0.5\\ & & \text{(U)}& 0.25\end{array}$

Which of the following is the only CORRECT combination?

1. $\left(A\right)\to \left(T\right)$
2. $\left(B\right)\to \left(P\right)$
3. $\left(C\right)\to \left(S\right)$
4. $\left(D\right)\to \left(Q\right)$

Q. What is a real valued function whose domain is the sample space of a random experiment called ?

Q. Ram rolls a fair die. Which of the following can be the outcome?

1. Head
2. Tail
3. 1
4. 2

Q.

Arun comes with a coin which has head on both the sides. He then tells 'I am going to conduct a random experiment by tossing this coin and seeing whether it is head or tail”. Statement: what Arun conducted was not a random experiment.

1. True

2. False

Q. $\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{Let}n\text{be a number chosen randomly from}& & \\ & \text{the set of first}100\text{natural numbers. Then}& & \\ & \text{the probability that the value of}(1+i{)}^n& & \\ & \text{is real, is}& \text{(P)}& 2\\ \text{(B)}& \text{If the coefficient of}{x}^{13}\text{in the expansion of}& & \\ & (1-x{)}^5(1+x+x^2+x^3{)}^4\text{is}k\text{, then the}& & \\ & \text{value of}\frac{k}{4}\text{is}& \text{(Q)}& 0.35\\ \text{(C)}& \text{In an examination of}9\text{papers, a candidate}& & \\ & \text{has to pass in more papers than (s)he fails in}& & \\ & \text{order to be successful. If the number of}& & \\ & \text{ways in which (s)he can be unsuccessful is}{2}^m,& & \\ & \text{then the value of}\frac{m}{4}\text{is}& \text{(R)}& 0.55\\ \text{(D)}& A,B,C\text{are three events such that}& & \\ & P\left(A\right)=0.6,P\left(B\right)=0.4,P\left(C\right)=0.5,& & \\ & P(A\cup B)=0.8,P(A\cap C)=0.3\text{and}& & \\ & P(A\cap B\cap C)=0.2\text{. If}P(A\cup B\cup C)\ge 0.85& & \\ & \text{and}P(B\cap C)\text{lies in the interval}[0.2,b]\text{,}& & \\ & \text{then the value of}b\text{is}& \text{(S)}& 1\\ & & \text{(T)}& 0.5\\ & & \text{(U)}& 0.25\end{array}$

Which of the following is the only CORRECT combination?

1. $\left(A\right)\to \left(T\right)$
2. $\left(B\right)\to \left(P\right)$
3. $\left(C\right)\to \left(S\right)$
4. $\left(D\right)\to \left(Q\right)$