## 1. If an event is certain to happen, its probability is:

### Answer:

### Explanation:

An event that is certain to happen has a probability of 1.

## 2. The probability of an impossible event is:

### Answer:

### Explanation:

An impossible event has a probability of 0.

## 3. In a single toss of a fair die, the probability of getting an even number is:

### Answer:

### Explanation:

There are 3 even numbers (2,4,6) out of 6 possible outcomes.

## 4. If P(A) represents the probability of event A, then 0 ≤ P(A) ≤ :

### Answer:

### Explanation:

Probability values range between 0 and 1, inclusive.

## 5. Two events that cannot occur at the same time are called:

### Answer:

### Explanation:

Mutually exclusive events are those that cannot occur simultaneously.

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

### Answer:

### Explanation:

There are 26 red cards (hearts and diamonds) out of a total of 52 cards.

## 7. If the probability of an event A happening is 0.2, the probability of A not happening is:

### Answer:

### Explanation:

Probability of not A = 1 – Probability of A = 1 – 0.2 = 0.8.

## 8. If two events A and B are independent, then P(A and B) is:

### Answer:

### Explanation:

For independent events, the probability of both occurring is the product of their individual probabilities.

## 9. The total number of outcomes when a coin is flipped and a die is rolled together is:

### Answer:

### Explanation:

2 outcomes for the coin (head or tail) and 6 for the die, so 2 x 6 = 12.

## 10. The probability of getting a sum of 7 when two dice are rolled is:

### Answer:

### Explanation:

The pairs (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) give a sum of 7. There are 6 favorable outcomes out of 36, so 6/36 = 1/6.

## 11. In a deck of cards, the probability of drawing a king or a queen is:

### Answer:

### Explanation:

There are 4 kings and 4 queens, so 8 favorable outcomes out of 52. Hence, 8/52 = 2/13.

## 12. If two events are mutually exclusive:

### Answer:

### Explanation:

Mutually exclusive events cannot occur at the same time, and their joint probability is 0.

## 13. The probability of a randomly chosen month having 31 days is:

### Answer:

### Explanation:

7 months have 31 days out of 12 months.

## 14. In a game, if you have a 90% chance of winning once, the probability of losing three times in a row is:

### Answer:

### Explanation:

The probability of losing once is 0.1, so losing three times in a row is 0.1 x 0.1 x 0.1 = 0.1^3.

## 15. If A and B are independent events and P(A) = 0.4, P(B) = 0.5, then P(A or B) is:

### Answer:

### Explanation:

P(A or B) = P(A) + P(B) – P(A and B) = 0.4 + 0.5 – (0.4 x 0.5) = 0.7.

## 16. The probability that a leap year chosen at random will have 53 Sundays is:

### Answer:

### Explanation:

Leap year has 366 days. 366 mod 7 = 2. So, the year can begin on any day but will have an extra day. There are 2 possibilities when Sunday will appear 53 times: if the year starts on a Saturday or a Sunday.

## 17. If P(A) = 0.3, P(B) = 0.4 and P(A and B) = 0.12, then the events A and B are:

### Answer:

### Explanation:

If A and B are independent, then P(A and B) = P(A) x P(B) = 0.3 x 0.4 = 0.12.

## 18. The probability of getting a total of 11 when two dice are rolled is:

### Answer:

### Explanation:

The pairs (5,6) and (6,5) give a total of 11. So, the probability is 2/36 or 1/18.

## 19. The probability of selecting a vowel from the English alphabet is:

### Answer:

### Explanation:

There are 5 vowels in the English alphabet out of 26 letters.

## 20. If two coins are tossed, the probability of getting at least one head is:

### Answer:

### Explanation:

Out of the four outcomes (HH, HT, TH, TT), three contain at least one head.