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.