# Worksheet: Simple Probability ## Section A: Multiple Choice Questions
Q1: A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4? (a) \(\frac{1}{6}\) (b) \(\frac{1}{3}\) (c) \(\frac{1}{2}\) (d) \(\frac{2}{3}\)
Solution:
Ans: (b) Explanation: The sample space contains 6 possible outcomes: {1, 2, 3, 4, 5, 6}. The favorable outcomes are numbers greater than 4: {5, 6}, which gives us 2 favorable outcomes. The probability is \(\frac{2}{6} = \frac{1}{3}\).
Q2: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability that it is NOT blue? (a) \(\frac{3}{10}\) (b) \(\frac{7}{10}\) (c) \(\frac{1}{2}\) (d) \(\frac{2}{5}\)
Solution:
Ans: (b) Explanation: The total number of marbles is 5 + 3 + 2 = 10. The number of marbles that are NOT blue is 5 + 2 = 7 (red and green marbles). Therefore, the probability is \(\frac{7}{10}\). This is also equal to \(1 - P(\text{blue}) = 1 - \frac{3}{10} = \frac{7}{10}\) using the complement rule.
Q3: Two coins are flipped simultaneously. What is the probability of getting exactly one head? (a) \(\frac{1}{4}\) (b) \(\frac{1}{3}\) (c) \(\frac{1}{2}\) (d) \(\frac{3}{4}\)
Solution:
Ans: (c) Explanation: The sample space for two coins is {HH, HT, TH, TT}, containing 4 equally likely outcomes. The favorable outcomes with exactly one head are {HT, TH}, which gives 2 favorable outcomes. The probability is \(\frac{2}{4} = \frac{1}{2}\).
Q4: A spinner is divided into 8 equal sections numbered 1 through 8. What is the probability of landing on a prime number? (a) \(\frac{3}{8}\) (b) \(\frac{1}{2}\) (c) \(\frac{5}{8}\) (d) \(\frac{1}{4}\)
Solution:
Ans: (b) Explanation: The prime numbers from 1 to 8 are {2, 3, 5, 7}, which gives 4 favorable outcomes. The total number of sections is 8. The probability is \(\frac{4}{8} = \frac{1}{2}\). Note that 1 is not a prime number.
Q5: What is the probability of randomly selecting a vowel from the word "PROBABILITY"? (a) \(\frac{4}{11}\) (b) \(\frac{5}{11}\) (c) \(\frac{3}{11}\) (d) \(\frac{6}{11}\)
Solution:
Ans: (a) Explanation: The word "PROBABILITY" has 11 letters. The vowels are O, A, I, I, giving us 4 vowels. The probability is \(\frac{4}{11}\). Note that we count each letter individually, even if it appears more than once.
Q6: Events A and B are mutually exclusive. If \(P(A) = 0.3\) and \(P(B) = 0.25\), what is \(P(A \text{ or } B)\)? (a) 0.075 (b) 0.55 (c) 0.50 (d) 0.35
Solution:
Ans: (b) Explanation: Since events A and B are mutually exclusive, they cannot occur at the same time, so \(P(A \text{ and } B) = 0\). Using the addition rule: \(P(A \text{ or } B) = P(A) + P(B) = 0.3 + 0.25 = 0.55\).
Q7: A standard deck of 52 playing cards contains 4 suits. What is the probability of drawing a King or a Queen? (a) \(\frac{1}{13}\) (b) \(\frac{2}{13}\) (c) \(\frac{1}{26}\) (d) \(\frac{4}{13}\)
Solution:
Ans: (b) Explanation: There are 4 Kings and 4 Queens in a standard deck, giving 8 favorable outcomes. The total number of cards is 52. The probability is \(\frac{8}{52} = \frac{2}{13}\). These events are mutually exclusive since a card cannot be both a King and a Queen.
Q8: If the probability of rain tomorrow is 0.35, what is the probability that it will NOT rain? (a) 0.35 (b) 0.50 (c) 0.65 (d) 0.70
Solution:
Ans: (c) Explanation: The events "rain" and "not rain" are complementary events. Using the complement rule: \(P(\text{not rain}) = 1 - P(\text{rain}) = 1 - 0.35 = 0.65\). Complementary events always sum to 1.
## Section B: Fill in the Blanks Q9: The set of all possible outcomes of an experiment is called the __________.
Solution:
Ans: sample space Explanation: The sample space is the fundamental concept in probability that lists all possible outcomes of a probability experiment. For example, when rolling a die, the sample space is {1, 2, 3, 4, 5, 6}.
Q10: If an event is impossible, its probability equals __________.
Solution:
Ans: 0 Explanation: An impossible event has no chance of occurring, so its probability is 0. For example, rolling a 7 on a standard six-sided die has probability 0.
Q11: Two events that cannot occur at the same time are called __________ events.
Solution:
Ans: mutually exclusive Explanation:Mutually exclusive events (also called disjoint events) have no outcomes in common and cannot happen simultaneously. For example, when flipping a coin, getting heads and getting tails are mutually exclusive.
Q12: The probability of a certain event is __________.
Solution:
Ans: 1 Explanation: A certain event is guaranteed to occur, so its probability equals 1. For example, the probability of rolling a number between 1 and 6 on a standard die is 1.
Q13: The formula for the probability of an event is: P(E) = \(\frac{\text{number of favorable outcomes}}{\text{__________}}\).
Solution:
Ans: total number of possible outcomes Explanation: This is the classical probability formula used when all outcomes are equally likely. The denominator represents the size of the sample space.
Q14: For any event A, the sum of P(A) and P(not A) equals __________.
Solution:
Ans: 1 Explanation: This represents the complement rule. Events A and "not A" are complementary and together make up the entire sample space, so their probabilities must sum to 1.
## Section C: Word Problems Q15: A survey of 200 students found that 120 students play sports, and 80 students do not play sports. If one student is chosen at random from this group, what is the probability that the student plays sports? Express your answer as a decimal.
Solution:
Ans: Step 1: Identify the total number of students: 200 Step 2: Identify the number of favorable outcomes (students who play sports): 120 Step 3: Calculate the probability: \(P(\text{plays sports}) = \frac{120}{200} = 0.6\) Final Answer: 0.6
Q16: A jar contains 8 chocolate chip cookies, 5 oatmeal cookies, and 7 sugar cookies. If Sarah randomly selects one cookie from the jar, what is the probability that she selects an oatmeal cookie? Express your answer as a simplified fraction.
Solution:
Ans: Step 1: Find the total number of cookies: 8 + 5 + 7 = 20 Step 2: Identify the number of oatmeal cookies: 5 Step 3: Calculate the probability: \(P(\text{oatmeal}) = \frac{5}{20} = \frac{1}{4}\) Final Answer: \(\frac{1}{4}\)
Q17: Marcus is playing a game where he spins a spinner divided into 10 equal sections numbered 1 through 10. He wins if he lands on a multiple of 3. What is the probability that Marcus wins? Express your answer as a simplified fraction.
Solution:
Ans: Step 1: Identify the sample space: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, total = 10 Step 2: Identify the multiples of 3: {3, 6, 9}, total = 3 Step 3: Calculate the probability: \(P(\text{wins}) = \frac{3}{10}\) Final Answer: \(\frac{3}{10}\)
Q18: A weather forecaster states that the probability of snow on Monday is 0.42. What is the probability that it will NOT snow on Monday? Express your answer as a decimal.
Solution:
Ans: Step 1: Identify that "snow" and "not snow" are complementary events Step 2: Apply the complement rule: \(P(\text{not snow}) = 1 - P(\text{snow})\) Step 3: Calculate: \(P(\text{not snow}) = 1 - 0.42 = 0.58\) Final Answer: 0.58
Q19: A box contains 12 red pens, 18 blue pens, and 15 black pens. If two events are defined as A = "selecting a red pen" and B = "selecting a blue pen," find P(A or B). Express your answer as a simplified fraction.
Solution:
Ans: Step 1: Find the total number of pens: 12 + 18 + 15 = 45 Step 2: Since A and B are mutually exclusive, use: \(P(A \text{ or } B) = P(A) + P(B)\) Step 3: Calculate: \(P(A) = \frac{12}{45}\) and \(P(B) = \frac{18}{45}\) Step 4: \(P(A \text{ or } B) = \frac{12}{45} + \frac{18}{45} = \frac{30}{45} = \frac{2}{3}\) Final Answer: \(\frac{2}{3}\)
Q20: In a class of 30 students, 18 students have brown eyes, 8 students have blue eyes, and 4 students have green eyes. If the teacher randomly selects one student to answer a question, what is the probability that the student has either blue or green eyes? Express your answer as a simplified fraction.
Solution:
Ans: Step 1: Total number of students = 30 Step 2: Number of students with blue or green eyes = 8 + 4 = 12 Step 3: Since "blue eyes" and "green eyes" are mutually exclusive events Step 4: Calculate: \(P(\text{blue or green}) = \frac{12}{30} = \frac{2}{5}\) Final Answer: \(\frac{2}{5}\)
The document Worksheet (with Solutions): Simple Probability is a part of the Grade 10 Course Integrated Math 2.
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