Finding Probability in case of Dependent Events

Q.

From a pack of $52$ cards, two cards are drawn in succession one by one without replacement. The probability that both are aces is

1. $\frac{2}{13}$

2. $\frac{1}{51}$

3. $\frac{1}{221}$

4. $\frac{2}{21}$

Q.

Two cards are drawn successively with replacement from a pack of $52$ cards. The probability of drawing two aces is

1. $\frac{1}{169}$

2. $\frac{1}{221}$

3. $\frac{1}{2652}$

4. $\frac{4}{663}$

Q. From a pack of 52 playing cards two cards are drawn at random without replacement. What is the probability of choosing both Face cards?

1. $\frac{11}{221}$
   
2. $\frac{1}{221}$
3. $\frac{33}{221}$
4. $\frac{9}{221}$

Q.

A Card is drawn randomly from a pack of playing cards. Then the probability that it is neither ace nor king is

1. $11/13$

2. $8/13$

3. $10/13$

4. $12/13$

Q.

A bag contains tickets numbered from $1$ and $20$. Two tickets are drawn. The probability that both the numbers are prime is

1. $\frac{14}{95}$

2. $\frac{7}{95}$

3. $\frac{1}{95}$

4. None of these

Q. Three cards are drawn one by one from a deck of $52$ playing cards without replacement. What is the probability of getting a King then an Ace and then a two?

1. $\frac{4}{52}\times \frac{4}{51}\times \frac{2}{50}$
2. $\frac{1}{13}\times \frac{4}{51}\times \frac{2}{25}$
3. $\frac{1}{13}\times \frac{1}{51}\times \frac{1}{50}$
4. All of the above.

Q. Four cards are drawn one by one from a deck of $52$ playing cards without replacement. What is the probability of getting a queen followed by a ten, an ace, and a two?

1. $\frac{1}{13}\times \frac{1}{13}\times \frac{1}{13}\times \frac{1}{13}$
2. $\frac{1}{13}\times \frac{4}{51}\times \frac{2}{25}\times \frac{4}{49}$
3. $\frac{1}{13}\times \frac{4}{51}\times \frac{2}{25}\times \frac{2}{25}$
4. $\frac{1}{13}\times \frac{4}{52}\times \frac{4}{52}\times \frac{4}{52}$

Q. From a standard deck of 52 cards two cards are drawn at random without replacement. What is the probability of getting both Ace?

1. ${\left(\frac{1}{17}\right)}^2$
2. ${\left(\frac{1}{13}\right)}^2$
3. $\frac{1}{221}$
4. None of the above

Q. Alex has 12 blue shirts and 12 white shirts. Everyday he picks one shirt at random for office. After he has used that shirt, he chooses another shirt at random and wears them.What is the probability that he first picks a white shirt then a blue?

1. $\frac{1}{4}$
2. $\frac{2}{23}$
3. $\frac{6}{23}$
4. $\frac{1}{6}$

Q. Teacher needs two students to help him with a science experiment for his class of 10 girls and 10 boys. He randomly picks two students one by one. What is the probability of choosing a boy then a girl?

1. $\frac{10}{19}$
2. $\frac{5}{19}$
3. $\frac{1}{4}$
4. $\frac{1}{10}$

Q. The table gives the information of boys and girls liking their favorite fruits. is likely to happen according to the given two way table.

1. (1, A)
2. (1, B)
3. (2, B)
4. (2, A)