Probability and Counting Principles Flashcards
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Read the first 6 Probability and Counting Principles flashcards as text
A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. What is the probability of drawing a blue marble?
Answer: 3/12
Total marbles = 4+3+5 = 12. P(blue) = 3/12 = 1/4. Note that 3/12 simplifies to 1/4, and answer choice C (3/12) equals answer choice B (1/4); the unreduced form 3/12 is the direct calculation.
Two fair six-sided dice are rolled. What is the probability that both show a number greater than 4?
Answer: 1/9
Numbers greater than 4 on one die: {5, 6} → probability = 2/6 = 1/3. For two independent dice: (1/3) × (1/3) = 1/9.
In how many ways can 5 students be arranged in a line?
Answer: 120
This is a permutation of 5 items: 5! = 5×4×3×2×1 = 120.
A committee of 3 is chosen from 7 people. How many different committees are possible?
Answer: 35
C(7,3) = 7!/(3!×4!) = (7×6×5)/(3×2×1) = 210/6 = 35.
If P(A) = 0.4 and P(B) = 0.3 and A and B are mutually exclusive, what is P(A or B)?
Answer: 0.7
For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.4 + 0.3 = 0.7.
A card is drawn from a standard 52-card deck. What is the probability that it is a king OR a heart?
Answer: 16/52
P(king) = 4/52, P(heart) = 13/52, P(king of hearts) = 1/52. P(king or heart) = 4/52 + 13/52 − 1/52 = 16/52 = 4/13.
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