Independent Events

Q.

What is the product rule in probability?

Q. Compound events in which the outcome of one does not affect the outcome of the other are known as independent events.

1. True
2. False

Q. The probability of drawing two red cards at random one after the other from a deck containing 52 cards with replacement is which type of event?

1. $\text{Independent}$
2. $\text{Dependent}$

Q. Which among the following probabilites of events is correctly matched with its respective type?

1. $\text{P(A and B)= P(A)}\times \text{P(B)}$,
   Dependent event
2. $\text{P(A and B)= P(A)}\times \text{P(B)}$, Independent event
3. $\text{P(A and B)= P(A)}\times \text{P(B)}$, where
   B knowing that A has occured.
   Independent Event

Q. Two events A and B are occuring simultaneously. Probability of occuring of event A is $0.4$ and probability of events A and B occuring together is $0.8$. What will be the probability of non - occurance of B event if replacement is allowed?

1. $0.2$
2. $0.8$
3. $0.4$
4. $1$

Q. Set up an equation in the following case:
Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (Take m to be the number of Parmit’s marbles.)

Q. Write the probability of choosing one marble from the following :

1. Choosing a red marble​

2. Choosing a yellow marble

Q. For two independent events A and B, $P\left(AandB\right)=$ . Fill in the blank with the correct representation.

1. $P\left(A\right)-P\left(B\right)$
2. $P\left(A\right)\times P\left(B\right)$
3. $P\left(A\right)+P\left(B\right)$

Q. A bag contains 4 pink, 10 white and 8 yellow marbles. Two marbles are drawn at random one after the other. Which type of event is this if both marbles drawn are yellow?

1. Dependent
2. Independent

Q. Which of the following are independent events?

1. Winning a card game and running out of bread.
2. Growing the perfect tomato and owning a cat.
3. Coloring the hair and cutting logs of wood.
4. $\text{P(E) = P(A) . P(B)}$