Introduction to Probability

Show your work for each problem.

1.
What is the probability of rolling a on a standard six-sided die?
1. a)
2. b)
3. c)
4. d)
Answer:
There is 1 favorable outcome (rolling a 3) out of 6 possible outcomes (1, 2, 3, 4, 5, 6). So the probability is .
2.
Which event has a probability of ?
1. a)Flipping heads on a coin
2. b)Rolling an odd number
3. c)Rolling a 7 on a standard die
4. d)Rolling a number less than 7
Answer: Rolling a 7 on a standard die
A standard die has only faces 1-6, so rolling a 7 is impossible. The probability is .
3.
What is the probability of flipping heads on a fair coin? Write your answer as a simplified fraction.
Answer: 1/2
A fair coin has 2 equally likely outcomes: heads and tails. There is 1 favorable outcome (heads). So the probability is .
4.
A bag contains 4 red marbles and 6 blue marbles. What is the probability of drawing a red marble? Write as a simplified fraction.
Answer: 2/5
Total marbles = 4 + 6 = 10. Red marbles = 4. Probability = .
5.
Which event has a probability of ?
1. a)Rolling a number less than 7 on a die
2. b)Rolling a 6 on a die
3. c)Flipping heads
4. d)Rolling an even number
Answer: Rolling a number less than 7 on a die
All faces (1, 2, 3, 4, 5, 6) are less than 7, so this event always happens. Probability = .
6.
A spinner has 8 equal sections: 3 red, 2 blue, and 3 green. What is the probability of landing on blue?
Answer: 1/4
1. How many blue sections are there? 2
2. How many sections are there in total? 8
3. Write the probability as a fraction: blue sections over total sections 2/8
4. Simplify the fraction by dividing both by 2 1/4
7.
What is the probability of rolling an odd number on a standard die? Write as a simplified fraction.
Answer: 1/2
Odd numbers: 1, 3, 5 (3 outcomes). Total: 6. Probability = .
8.
A bag has 5 red, 3 blue, and 2 yellow marbles. What is the probability of NOT drawing a red marble?
1. a)
2. b)
3. c)
4. d)
Answer:
Not red = blue + yellow = 3 + 2 = 5 marbles. Total = 10. Probability = .
9.
A deck has 4 aces in 52 cards. What is the probability of drawing an ace? Simplify your answer.
Answer: 1/13
1. How many aces (favorable outcomes) are there? 4
2. How many cards (total outcomes) are there? 52
3. Write the probability as a fraction 4/52
4. What is the GCF of 4 and 52? 4
5. Simplify by dividing both by the GCF 1/13
10.
Express the probability as a percentage.
Answer: 60
11.
A box contains 6 red balls, 4 blue balls, and 5 green balls. What is the probability of drawing a ball that is NOT green?
Answer: 2/3
1. What is the total number of balls? 15
2. How many balls are NOT green? 10
3. Write the probability as a fraction 10/15
4. Simplify by dividing both by 5 2/3
12.
The probability of an event is . What is the probability that the event does NOT happen? Write as a decimal.
Answer: 0.65
13.
Which statement about probability is FALSE?
1. a)A certain event has probability 1
2. b)An impossible event has probability 0
3. c)Probability ranges from 0 to 1
4. d)If you flip heads 5 times in a row, tails is more likely on the next flip
Answer: If you flip heads 5 times in a row, tails is more likely on the next flip
Each coin flip is independent. Past results don't affect future flips. The probability of tails is still , not higher. This mistake is called the gambler's fallacy.
14.
A jar contains 8 white marbles, 6 black marbles, and 4 gray marbles. If you randomly pick one marble, what is the probability it is white or gray?
Answer: 2/3
1. What is the total number of marbles? 18
2. How many marbles are white? 8
3. How many marbles are gray? 4
4. How many marbles are white OR gray? 12
5. Write the probability as a simplified fraction 2/3
15.
In a survey, 25 students like math, 15 like science, and 10 like both. If a student is chosen at random from the 30 total students surveyed, what is the probability they like math but NOT science?
Answer: 1/2
1. How many students like math in total? 25
2. How many students like BOTH math and science? 10
3. How many students like math but NOT science? 15
4. What is the total number of students? 30
5. Write the probability as a simplified fraction 1/2