Probability of Simple Events — 7th Math: Statistics & Probability practice questions

A coin is tossed 1,000 times and lands heads 510 times. What does the result suggest?

1. The coin is biased toward heads
2. The coin is biased toward tails
3. Results are very close to theoretical fairness; no strong evidence of bias
4. The coin can never land tails again

Answer: C — Results are very close to theoretical fairness; no strong evidence of bias

51% vs 50% in 1,000 trials is within normal variation. (A/B) overreach; (D) gambler's fallacy.

A bag has 7 balls: 3 red, 2 blue, 2 green. P(red OR blue)?

1. 5/7
2. 6/49
3. 3/7
4. 2/7

Answer: A — 5/7

Mutually exclusive: P(red) + P(blue) = 3/7 + 2/7 = 5/7. (B) treats as AND; (C) only red; (D) only blue.

P(rolling an even number on a fair 6-sided die) =

1. 1/6
2. 2/6
3. 1/3
4. 1/2

Answer: D — 1/2

D) Events 2, 4, 6 → 3/6 = 1/2. A) One face only. B) Two of three. C) Reduced 2/6 incorrectly.

Rolling a 6-sided die: P(rolling an even number OR rolling a 5)?

1. 3/6
2. 1/2
3. 2/3
4. 5/6

Answer: C — 2/3

Even: {2,4,6} = 3 outcomes; 5 is odd and not in even set (mutually exclusive): add 1 → 4 total / 6 = 2/3. (A) only counts even numbers; (B) only 3 out of 6; (D) overcounts.

You flip a fair coin 10 times and get 8 heads. What is the BEST conclusion?

1. The coin must be unfair
2. Theoretical P(heads) is now 8/10
3. Experimental P(heads) was 0.8, but 10 flips is a small sample — theoretical P(heads) is still 1/2
4. The next flip must be tails

Answer: C — Experimental P(heads) was 0.8, but 10 flips is a small sample — theoretical P(heads) is still 1/2

Small samples can deviate from theoretical probability without proving unfairness. (A) overreach; (B) confuses experimental with theoretical; (D) gambler's fallacy — independent flips have no memory.

The probability of an event ranges from:

1. Any real number
2. −1 to 1
3. 0 to 1 (inclusive)
4. 0 to 100 only

Answer: C — 0 to 1 (inclusive)

C) Probability is bounded. A) Unbounded is incorrect. B) Negative probability is undefined. D) Percent vs. proportion form.

A weather forecast says 'P(rain) = 70% tomorrow'. The most accurate interpretation is:

1. It will definitely rain
2. On 70% of similar past days, it has rained — so rain is likely
3. It will rain 70% of the day
4. Rain is impossible

Answer: B — On 70% of similar past days, it has rained — so rain is likely

Forecast probability reflects long-run frequency on comparable days. (A) overstates; (C) misreads probability as duration; (D) contradicts the number.

An event with probability 0 is:

1. Impossible
2. Certain
3. Likely
4. Random

Answer: A — Impossible

A) P = 0 means cannot occur. B) Certainty is P = 1. C/D) Don't map to P = 0.

Data set: {5, 8, 8, 9, 10}. The mean is:

1. 8
2. 8.5
3. 9
4. 40

Answer: A — 8

Mean = (5+8+8+9+10)/5 = 40/5 = 8. (B) median; (C) largest minus middle; (D) forgot to divide by 5.

A class did 50 trials of drawing a colored card from a deck. Red came up 22 times. The estimated P(red) from this experiment is closest to:

1. 0.22
2. 0.78
3. 0.50
4. 0.44

Answer: D — 0.44

Experimental P = 22/50 = 0.44. (A) misreads count as proportion; (C) theoretical for red in a standard deck; (B) 1 − 0.22.

What does probability of 1 mean?

The event WILL happen for sure.

On a fair die, P(rolling a number 1-6)?

1 (certain).

Worked example: A bag has 3 red, 4 blue, 5 green marbles. Find P(red).

Step 1: Find the total number of marbles: 3 + 4 + 5 = 12. Step 2: Identify favorable outcomes — red marbles = 3. Step 3: Apply P = favorable / total = 3/12. Step 4: Simplify the fraction: 3/12 = 1/4. Answer: P(red) = 3/12 = 1/4 (25%).

What's the probability formula?

P(event) = number of favorable outcomes / total possible outcomes.