Independent Events

Q.

Two fair dice are tossed. Let $A$ be the event that the first die shows an even number and $B$ be the event that the second die shows an odd number. The two events $A$ and $B$ are

1. Mutually exclusive

2. Independent and mutually exclusive

3. Dependent

4. None of the above

Q.

I forgot the last three digits of a 7-digit telephone number. If I randomly dial the final 3 digits after correctly dialling the first four, then what are the chances of dialling the correct number?

1. None of these

2. 1/1000

3. 1/990

4. 1/720

5. 1/100

Q. When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less or equal to 10?

1. 
2. 
3. 
4. 

Q. 4 out of 15 apples are rotten. They are taken out one by one at random and examined. The ones which are examined are not replaced. What is the probability that the 9${}^{th}$ one examined is the last rotten one?

1. 
2. 
3. 
4. none of these

Q.

A bag contains $5$ white, and $3$ black balls and four balls are sucessively drawn out and not replaced. The probability that they are alternately of different colours, is

1. $\frac{1}{196}$

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

3. $\frac{1}{7}$

4. $\frac{13}{56}$

Q.

If five dice are thrown simultaneously, then what is the probability of getting the sum of the numbers as seven?

1. 15/(6⁵)

2. 10/(6⁵)

3. 15/(5⁶)

4. 10/(5⁶)

5. None of these

Q.

What is the probability of getting two numbers whose product is odd when two dice are thrown simultaneously?

1. none

2. 1/2

3. 1/4

4. 7/8

5. 3/8

Q.

The probability of success of three students Karan, Sarosh and Vignesh in the one examination are $\frac{1}{5}$, $\frac{1}{4}$ and $\frac{1}{3}$ respectively.
What is the probability that at least two of them will be successful?

1. $\frac{1}{6}$

2. $\frac{2}{5}$

3. $\frac{3}{5}$

4. $\frac{3}{5}$

5. None of these

Q.

A ticket is picked up randomly from tickets numbered 1 to 20. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

1. 9/20

2. none

3. 11/20

4. 13/20

5. 1/2

Q. If P = {x: x is an even number} and Q = {y: y is an odd number}, then PUQ is

1. Set of rational numbers
2. Set of integers
3. Set of whole numbers
4. Set of natural numbers

Q.

A coin and six faced die, both unbiased are thrown simultaneously. The probability of getting a tail on the coin and an even number on the die is:

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

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

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

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

Q.

A man succeeds twice as often as he fails. What is the probability that in the next 5 trials there will be four successes?

1. 

2. 

3. 

4. 

Q. A wooden cask contains some tools i.e. exactly 12 nuts and 24 bolts. ${\left(\frac{1}{3}\right)}^{rd}$ of each of these are defective. If 2 tools are picked up one after the other without replacement, then what is the probability that both are not defective?

1. 
2. 
3. 
4. 

Q. If A = {x: x is an odd number} and B = {y: y is a natural number}, then find A-B

1. Set of even numbers
2. Set of natural numbers
3. None of these
4. Null set

Q.

Find the probability of getting a multiple of 3 on one die and multiple of 2 on the other die when two dice are thrown simultaneously?

1. 13/36

2. 11/36

3. 7/36

4. 5/9

5. None of these

Q. When 2 dice are thrown simultaneously, the probability that the sum of numbers is 12 is ‘x’. The value of ‘180x’ = _____________.

Q.

3 cards are drawn from a pack of 52 cards. What is the probability that one is ace, one is queen and one is jack?

1. None of these

2. 13/5525

3. 14/5525

4. 15/5525

5. 16/5525

Q.

A deck of $52$ cards is shuffled and dealt .

Find the probabilities of the following events:

The last king appears on the ${48}^{th}$ card.

Q.

A man succeeds twice as often as he fails. What is the probability that in the next 5 trials there will be four successes?

1. (2/3)⁴*(1/3)

2. None of these

3. 5*(2/3)*(1/3)⁴

4. (2/3)*(1/3)⁴

5. 5*(2/3)⁴*(1/3)