Introduction to Probability

Q. An uncertain event is an event whose outcome cannot be determined with absolute certainty.

1. True
2. False

Q.

There are $6$ marbles in a box with numbers from $1$ to $6$ marked on each of them.

What is the probability of drawing a marble with the number $2$?

Q. An event whose outcome cannot be predicted with 100% certainty is known as

1. Certain Event
2. Uncertain Event
3. Exhustive Event
4. Compound Event

Q. The measure of how likely it is for an event to occur is called probability.

1. True
2. False

Q. What is the probability of rolling a fair die and getting a 5?

1. $P\left(5\right)=\frac{1}{3}$
2. $P\left(5\right)=\frac{1}{4}$
3. $P\left(5\right)=\frac{1}{5}$
4. $P\left(5\right)=\frac{1}{6}$

Q. What is the probability of rolling a fair die and getting a 7?

1. $P\left(7\right)=\frac{1}{6}$
2. $P\left(7\right)=\frac{1}{2}$
3. $P\left(7\right)=\frac{5}{6}$
4. $P\left(7\right)=0$

Q.

There is an urn containing $10$ marbles numbered $1$ to $10$.

We sample $4$ marbles without replacement.

What is the probability that our sample contains the marbles labeled $1$ and $2$.

Q. A certain event is an event which is sure to happen.

1. True
2. False

Q. A $6$-sided die is rolled. What is the probability of rolling a number less than $8$?

Q.

A bag contains $7$ marbles: $3$ black, $2$ white and $2$ red. If you put your hand in the bag and draw out one marble, then what is the number of outcomes favoring white marbles?

Q. Events that are guaranteed to occur 100% of the time are known as

1. Uncertain Events
2. Certain Events
3. Compound Events
4. Exhaustive Events

Q.

A bag contains $7$ marbles: $3$ black, $2$ white and $2$ red. If you put your hand in the bag and draw out one marble, then state the probability of getting a black marble, i.e $P\left(black\right)$.

Q. The probablity of getting a heads on flipping a fair coin for the first time is:

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

Q. Which of the following involves probability?

1. Forecasting Weather
2. Optimising Profits
3. Making Business Decisions
4. All of the above.

Q.

A bag contains $7$ marbles: $3$ black, $2$ white and $2$ red. If you put your hand in the bag and draw out one marble, then state the number of outcomes favoring black marbles.

Q. A regular coin will always land on a heads or a tails is an example of a certain event.

1. True
2. False

Q. The probability of obtaining a head and a tail simultaneously when we toss a coin is

Q.

A bag contains $7$ marbles: $3$ black, $2$ white and $2$ red. If you put your hand in the bag and draw out one marble, then find $P(notblack)$?

Q. A teacher chooses a student at random from a class of $20$ boys. What is the probability that the student chosen is a boy?

1. $1$
2. $\frac{1}{20}$
   
3. $20$
4. $0$