## 1. What is the probability of a certain event?

### Answer:

### Explanation:

A certain event is an event that will always happen, so its probability is 1.

## 2. If an event cannot happen at all, its probability is:

### Answer:

### Explanation:

An impossible event has a probability of 0.

## 3. The probability of getting a head when a fair coin is tossed is:

### Answer:

### Explanation:

There are two possible outcomes: head or tail. Only one of them is a head. So, the probability is 1/2 or 0.5.

## 4. What is the sum of the probabilities of all possible outcomes of an experiment?

### Answer:

### Explanation:

The sum of the probabilities of all possible outcomes of an experiment is always 1.

## 5. The probability of an event E happening is 0.3. What is the probability that the event E does not happen?

### Answer:

### Explanation:

The probability of an event not happening is 1 minus the probability of the event happening. So, 1 – 0.3 = 0.7.

## 6. If a die is rolled, the probability of getting an even number is:

### Answer:

### Explanation:

The even numbers on a die are 2, 4, and 6. So, 3 out of 6 outcomes are even, giving a probability of 3/6 or 1/2.

## 7. The probability of an event that is certain not to happen is:

### Answer:

### Explanation:

An event that is certain not to happen has a probability of 0.

## 8. In a single throw of a pair of dice, the probability of getting a total of 7 is:

### Answer:

### Explanation:

There are 6 ways to get a total of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are 36 possible outcomes, so the probability is 6/36 or 1/6.

## 9. The probability of drawing a red card from a standard deck of cards is:

### Answer:

### Explanation:

There are 26 red cards (hearts and diamonds) in a deck of 52. So, the probability is 26/52 or 1/2.

## 10. If two coins are tossed simultaneously, the probability of getting at least one tail is:

### Answer:

### Explanation:

The possible outcomes are HH, HT, TH, and TT. Three of these have at least one tail, so the probability is 3/4.

## 11. An event having only one outcome is called:

### Answer:

### Explanation:

A simple event is an event having only one outcome.

## 12. The probability of drawing a face card (King, Queen, or Jack) from a standard deck of cards is:

### Answer:

### Explanation:

There are 12 face cards in a deck of 52, which gives a probability of 12/52 or 3/13.

## 13. The probability of getting a 5 when a die is rolled is:

### Answer:

### Explanation:

There is only one 5 on a die, and there are 6 possible outcomes. So, the probability is 1/6.

## 14. The probability of drawing a black queen from a standard deck of cards is:

### Answer:

### Explanation:

There are 2 black queens in a deck of 52 cards, so the probability is 2/52 or 1/26. However, the question asks for just one black queen, so it is 1/52.

## 15. If P(E) is the probability of an event E happening, then 0 ≤ P(E) ≤:

### Answer:

### Explanation:

The probability of any event lies between 0 (impossible) and 1 (certain).

## 16. The probability of getting a multiple of 3 when a die is rolled is:

### Answer:

### Explanation:

The multiples of 3 on a die are 3 and 6. So, 2 out of 6 outcomes are multiples of 3, giving a probability of 2/6 or 1/3.

## 17. A bag contains 5 red balls and 7 green balls. The probability of drawing a green ball is:

### Answer:

### Explanation:

There are 7 green balls out of a total of 12 balls. So, the probability is 7/12.

## 18. An event with zero probability is termed as:

### Answer:

### Explanation:

An event with zero probability is termed as impossible.

## 19. The probability that February has 29 days is:

### Answer:

### Explanation:

February has 29 days once every 4 years because of the leap year. So, the probability is 1/4.

## 20. The sum of the probabilities of an event and its complement is:

### Answer:

### Explanation:

The probability of an event and its complement always adds up to 1.