Compound Events [ P(A or B), P( A and B) ]

Q. A jar contains 2 green marbles, 4 blue marbles, 3 yellow marbles and 2 black marbles. A marble is chosen at random from the jar and replaced. Then a second marble is chosen at random. What is the probability of the first marble being green and the second marble being yellow?

1. $\frac{3}{121}$
2. $\frac{4}{121}$
3. $\frac{5}{121}$
4. $\frac{6}{121}$

Q.

Three numbers are chosen at random from $1$ to $20$. The probability that they are consecutive, is

1. $\frac{1}{190}$

2. $\frac{1}{120}$

3. $\frac{3}{190}$

4. $\frac{5}{190}$

Q. If two coins are tossed simultaneously, then what is the probability of getting exactly two tails?

1. $\frac{1}{4}$
2. $\frac{1}{3}$
3. $\frac{1}{2}$
4. None of the above

Q. All independent events are compound events but all compound events are not independent events.

1. True
2. False

Q. In a box, there are $3$ red marbles, $2$ green marbles and $7$ blue marbles. Oliver picks a marble blindfolded. What is the probability of picking a red marble or a green marble?

1. $\frac{3}{12}$
2. $\frac{5}{12}$
3. $\frac{7}{12}$
4. $\frac{4}{12}$

Q. Boucher rolls two dice sequentially. What is the probability of rolling 4 first then a number less than 3?

1. $\frac{1}{18}$
2. $\frac{1}{6}$
3. $\frac{1}{3}$
4. $\frac{5}{18}$

Q. $\text{P(A and B) = P(A)}\times \text{P(B)}$ is valid for both independent and dependent compound events.

1. True
2. False

Q. Events that consist of two or more single events are called compound events.

1. True
2. False

Q. Which of the following option resembles $\text{P(A or B)}$ and $\text{P(A and B)}$, respectively?

1. $\text{P(A)+P(B)}$ and $\frac{\text{P(A)}}{\text{P(B)}}$
2. $\text{P(A)-P(B)}$ and $\frac{\text{P(A)}}{\text{P(B)}}$
3. $\text{P(A)+P(B)}$ and $\text{P(A)}\times \text{P(B)}$
4. $\text{P(A)-P(B)}$ and $\text{P(A)}\times \text{P(B)}$