Random Experiment

Q. Two fair coins are tossed once. Then the number of elements in the sample space is

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.

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

1. False
2. True

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

Which of the following is the only INCORRECT combination?

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

Q. I toss a coin which has tails on both the sides, and record the outcome. The above mentioned experiment is a random experiment.

1. True
2. False

Q. Let’s say we keep 1 kg of water on a flickering flame. And we keep on recording the temperature of the water after every 30 seconds.
The above mentioned experiment is a random experiment.

1. True
2. False

Q. Selecting a blue ball from a bag which contains 50 blue balls is an example of a random experiment.

1. False
2. True