Introduction To Probability — Important Questions

0.7

Step 1: Recall the complement rule: P(E) + P(not E) = 1. Step 2: Given that P(E) = 0.3. Step 3: Substitute in the formula: 0.3 + P(not E) = 1. Step 4: Solve for P(not E): P(not E) = 1 - 0.3 = 0.7.

3/4

Step 1: List all possible outcomes: HH, HT, TH, TT (total = 4). Step 2: Identify outcomes with at least one head: HH, HT, TH (favorable = 3). Step 3: Apply probability formula: P(at least one head) = 3/4. Alternative method: P(at least one head) = 1 - P(no heads) = 1 - P(TT) = 1 - 1/4 = 3/4.

1/3

Step 1: List all possible outcomes on a die: 1, 2, 3, 4, 5, 6 (total = 6). Step 2: Identify numbers greater than 4: 5 and 6 (favorable = 2). Step 3: Apply probability formula: P(number > 4) = 2/6. Step 4: Simplify the fraction: 2/6 = 1/3.

5/12

Step 1: Calculate total number of balls: 5 white + 7 black = 12 balls. Step 2: Number of white balls = 5. Step 3: Apply probability formula: P(white) = 5/12. Step 4: The fraction 5/12 is already in simplest form, so the answer is 5/12.