Probability without Replacement (Dependent Events)

Q. Two cards are randomly chosen one after the other from a standard deck of $52$ playing cards without replacement. What is the probability of choosing two kings?

1. $\frac{1}{169}$
2. $\frac{4}{663}$
3. $\frac{1}{221}$
4. $\frac{3}{676}$

Q. In a box, there are 3 red pens, 2 green pens and 1 blue pen. Johan picks a pen blindfoldly. The probability of picking a red pen or a green pen is .

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

Q. The letters that form the word $\text{ALGEBRA}$ are placed in a bowl. The probability of picking a letter other than “A” is.

1. $\frac{2}{7}$
2. $\frac{5}{7}$
3. $\frac{1}{7}$
4. $\frac{6}{7}$

Q.

In throwing a die the number of possible outcomes is ______.

Q.

A word consists of $11$ letters in which there are $7$ consonants and $4$ vowels. If $2$ letters are chosen at random, then the probability that all of them are consonants is

1. $\frac{5}{11}$

2. $\frac{21}{55}$

3. $\frac{4}{11}$

4. None of these

Q. Lewis rolls a number cube that has sides labelled 1 to 6 and then flips a coin. The probability that Lewis rolls an even number and flips a head is .

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

Q. A box contains 6 white, 7 purple and 3 black balls. Balls are picked randomly one at a time without replacement. Prob. (picking purple then black) is.

1. $\frac{21}{256}$
2. $\frac{3}{16}$
3. $\frac{7}{80}$
4. $\frac{7}{16}$

Q.

You roll a number cube. What are the odds that you will roll an even number?

Q. A box has $2$ blue and $3$ yellow buttons of the same size. Two buttons are chosen at random without replacement. What is the probability that both are blue?

1. $\frac{2}{5}$
2. $\frac{1}{5}$
3. $\frac{1}{10}$
4. None of the above

Q.

Mathew rolls a number cube labeled with the numbers $1$ to $6$.

He then flips a fair coin.

What is the probability that he rolls a $4$ and flips a head?

Q. In a purchase of 100 Bulbs, 4 are defective. Two bulbs are randomly selected for inspection. What is the probability that both bulbs are defective if the first bulb is not replaced after inspecting?

1. $\text{P(E)}=\frac{4}{825}$
2. $\text{P(E)}=\frac{2}{285}$
3. $\text{P(E)}=\frac{1}{825}$
4. $\text{P(E)}=\frac{3}{582}$

Q. A college survey found that 6 out of 24 students walk to college. If 3 students are selected at random without replacement, what is the probability that all 3 walk to college?

1. $\text{P(E)}=\frac{23}{506}$
2. $\text{P(E)}=\frac{5}{506}$
3. $\text{P(E)}=\frac{1}{506}$
4. $\text{P(E)}=\frac{1}{605}$

Q. Inside a box, there are $8$ tickets of $3$ colors; $4$ are purple, $3$ are blue and $1$ gold. Two tickets are picked from the box at random without replacement. What is the probability that both the tickets are not purple?

1. $\frac{2}{7}$
2. $\frac{3}{4}$
3. $\frac{3}{14}$
4. $\frac{11}{14}$

Q. In a class test, 8 out of 30 students got full marks. If three students are chosen at random, what is the probability that all three got full marks?

1. $\text{P(E)}=\frac{4}{15}\times \frac{7}{29}\times \frac{3}{14}$
   
2. $\text{P(E)}={\left(\frac{4}{15}\right)}^3$
   
3. $\text{P(E)}=\frac{8}{30}\times \frac{7}{29}\times \frac{7}{28}$
   
4. (a) and (b) above.

Q. A bag contains 20 green marbles and 12 blue marbles. Four marbles are drawn at random. What is the probability of getting all green marbles?

1. $\text{P(E)}=\frac{95}{248}\times \frac{51}{145}$
2. $\text{P(E)}=\frac{323}{248}\times \frac{51}{145}$
3. $\text{P(E)}=\frac{15}{248}\times \frac{95}{145}$

Q. A die is rolled and a coin is tossed one after the other. What is the probability of rolling 1 and flipping a head or rolling 6 and flipping a tail?

Q. A coin is tossed and a die is rolled one after the other. The probability of flipping a tail and seeing a 4 or flipping a head and seeing a 6 is .

1. $\frac{1}{6}$
2. $\frac{2}{3}$
3. $\frac{1}{12}$

Q. 16 people are their in a college cricket team. 6 of them are batsman and 10 of them are bowlers. Two people are chosen at random. Calculate the probability that first is a batsman and second is bowler(without replacement).

1. $\text{P(A and B)}=\frac{1}{4}$
2. $\text{P(A and B)}=\frac{3}{8}$
3. $\text{P(A and B)}=\frac{2}{3}$
4. $\text{P(A and B)}=\frac{3}{4}$

Q.

An integer is chosen at random from $1$ to $50$. Find the probability that the number is a perfect cube.