Probability — Important Questions

Getting a 7 on a standard die, Drawing a red card from a deck of only black cards, Drawing a card with number 15 from a standard deck

Impossible events have probability 0. A standard die only has numbers 1-6 (no 7), a deck of only black cards has no red cards, and standard cards don't have number 15. Getting heads on a coin and even numbers on a die are possible events.

1/2

Prime numbers from 1 to 8 are: 2, 3, 5, 7 (that's 4 numbers). Total outcomes = 8. P(prime) = 4/8 = 1/2. Remember: 1 is not a prime number, and prime numbers have exactly two factors.

1/2

Possible outcomes when tossing two coins: HH, HT, TH, TT (4 total outcomes). Exactly one head occurs in: HT, TH (2 favorable outcomes). P(exactly one head) = 2/4 = 1/2.

0.7, 0, 1

Probability values must satisfy 0 ≤ P(E) ≤ 1. Valid probabilities: 0.7 (between 0 and 1), 0 (impossible event), 1 (certain event). Invalid: 1.2 (greater than 1), -0.3 (negative value). Probabilities cannot be negative or greater than 1.