Practice Questions
A coin is tossed twice. What is the probability of getting at least one head?
Total outcomes = $2^2 = 4$. No heads (TT) = 1 outcome. P(at least one head) = $1 - 1/4 = 3/4$.
A die is rolled once. What is the probability of getting a number greater than 4?
Numbers > 4: {5, 6} = 2 outcomes. Total = 6. Probability = $2/6 = 1/3$.
Two dice are thrown. What is the probability that the sum is 7?
Favorable pairs: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6. Total = 36. Probability = $6/36 = 1/6$.
A bag contains 5 red and 3 blue balls. Two balls are drawn randomly. What is the probability both are red?
P(both red) = $\\frac{5}{8} \\times \\frac{4}{7} = \\frac{20}{56} = \\frac{5}{14}$.
A card is drawn from a well-shuffled deck. What is the probability of getting a face card?
Face cards: Jack, Queen, King in each of 4 suits = $3 \times 4 = 12$. Total = 52. P(face card) = $12/52 = 3/13$.
Three coins are tossed. What is the probability of getting at least two heads?
Total outcomes = $2^3 = 8$. Favorable (2+ heads): HHT, HTH, THH, HHH = 4. Probability = $4/8 = 1/2$.
A bag contains 5 red, 4 blue and 3 green balls. Two balls are drawn at random. What is the probability that both are red?
Total balls = 12. P(first red) = $5/12$. P(second red | first red) = $4/11$. P(both red) = $5/12 \times 4/11 = 20/132 = 5/33$.
A card is drawn from a deck and replaced, then another is drawn. What is the probability both are kings?
P(king) = $4/52 = 1/13$. Since replaced, events are independent. P(both kings) = $1/13 \times 1/13 = 1/169$.
A student answers a 5-question true/false test randomly. What is the probability of getting exactly 4 correct answers?
Total outcomes = $2^5 = 32$. Ways to choose 4 correct = $\binom{5}{4} = 5$. Probability = $5/32$.
Two dice are thrown. What is the probability of getting a sum greater than 9?
Favorable sums > 9: sum 10: (4,6),(5,5),(6,4) = 3; sum 11: (5,6),(6,5) = 2; sum 12: (6,6) = 1. Total = 6. Probability = $6/36 = 1/6$.
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