Probability — Important Questions

1/13

Step 1: Identify total number of cards in a deck = 52. Step 2: Count the number of Aces in a deck. There are 4 Aces (one in each suit: spades, hearts, diamonds, clubs). Step 3: Apply probability formula P(Ace) = Number of Aces / Total cards. Step 4: Calculate P(Ace) = 4/52 = 1/13. We simplify 4/52 by dividing both numerator and denominator by 4 to get 1/13.

0.3

Step 1: Recall the complementary events formula: P(E) + P(not E) = 1. Step 2: Rearrange to find P(not E): P(not E) = 1 - P(E). Step 3: Substitute the given value P(E) = 0.7. Step 4: Calculate P(not E) = 1 - 0.7 = 0.3. This makes sense because if an event has 70% chance of occurring, it has 30% chance of not occurring.

3/4

Step 1: List all possible outcomes when two coins are tossed: (H,H), (H,T), (T,H), (T,T). Total outcomes = 4. Step 2: Identify outcomes with at least one head: (H,H), (H,T), (T,H). Favorable outcomes = 3. Step 3: Apply probability formula P(at least one head) = Favorable outcomes / Total outcomes. Step 4: Calculate P = 3/4. Alternative method: P(at least one head) = 1 - P(no heads) = 1 - P(both tails) = 1 - 1/4 = 3/4.

5/12

Step 1: Count total marbles in the box: 5 white + 7 black = 12 marbles. Step 2: Count favorable outcomes for white marble: 5 white marbles. Step 3: Apply probability formula P(white) = Number of white marbles / Total marbles. Step 4: Calculate P(white) = 5/12. This fraction cannot be simplified further since 5 and 12 have no common factors other than 1.