Probability — Important Questions

4/8

Step 1: Total sections on spinner = 8 sections numbered {1, 2, 3, 4, 5, 6, 7, 8}. Step 2: Even numbers among these = {2, 4, 6, 8} = 4 favorable outcomes. Step 3: Apply probability formula P(even number) = 4/8 = 1/2. Step 4: Note that 4/8 = 1/2, so both representations are correct. Half of the numbers from 1 to 8 are even, which makes intuitive sense.

3/6

Step 1: List all outcomes on a dice = {1, 2, 3, 4, 5, 6} = 6 total outcomes. Step 2: Identify prime numbers (numbers with exactly two factors: 1 and itself). Prime numbers on dice = {2, 3, 5} = 3 favorable outcomes. Step 3: Note that 1 is not prime, 4 and 6 are composite numbers. Step 4: P(prime number) = 3/6 = 1/2. Common mistake: Including 1 as prime number.

1/13

Step 1: Total cards in a standard deck = 52 cards. Step 2: Number of kings in deck = 4 kings (one in each suit: hearts, diamonds, clubs, spades). Step 3: Apply probability formula P(king) = 4/52. Step 4: Simplify the fraction: 4/52 = 1/13. Both 4/52 and 1/13 are correct, but 1/13 is the simplified form. Note that there are 13 different ranks in cards.

2/15

Step 1: Total balls = 4 white + 6 black = 10 balls. Step 2: Total ways to draw 2 balls from 10 = C(10,2) = 10×9/(2×1) = 45 ways. Step 3: Ways to draw 2 white balls from 4 white balls = C(4,2) = 4×3/(2×1) = 6 ways. Step 4: P(both white) = 6/45 = 2/15. Alternative method: P = (4/10) × (3/9) = 12/90 = 2/15.