Draw a probability line with a scale in decimals between 0 and 1. Place each of the following
events by its letter in a reasonable place on the line.
a. A person selected at random has a birthday in the summer (June, July, or August)
b. A person selected at random has a birthday today
c. A person selected at random does NOT have a summer birthday.
2. A hospital fundraising lottery claims that 1 in 7 people will win a prize. Show this probability
statement as a fraction, and percent (to two decimal places)
3. A dark cloth bag contains the following marbles: 10 red, 5 blue, 3 green. When you select
one marble without looking...
a. What is the theoretical probability of getting a blue marble? Express your answer as a
decimal value to three places.
b. What is the theoretical probability that the marble is NOT green? Express your answer
as a fraction in lowest terms.
4. A special board game comes with a die that has 8 faces, numbered 1
through 8. (This is called an octahedron). Your friend rolls a “3”. What is
the theoretical probability that you will roll a number greater than 3?
Express your answer as a percent, to one decimal place.
5. Joey has a pair of four-sided dice (tetrahedrons). Complete the chart below to show all the
sums possible when this pair of dice are rolled together.
Use this chart to determine the theoretical probability of rolling the sum of 6. Express your
answer as a decimal to three places.
6. Suppose you are going to spin each of these spinners once. Create a tree diagram to show all
the possible outcomes of one spin after the other. Use the tree diagram to determine the
theoretical probability of getting AT LEAST ONE blue. Express your answer as a fraction in
lowest terms.
7. The four graphs given below show the experimental and theoretical probabilities (in percent)
for a situation where a marble is selected from a bag of marbles and the colour is noted, over
an increasing number of trials. One of these graphs is correct and three are wrong. Which
graph is most likely to be correct. Give a reason for your choice.
8. Tell me one more thing that you know about probability and that you thought might be on this
assignment, but wasn’t.
BTW I am a grade 11 student
impatient much?
That's quite a laundry list you have there.
what have you done so far?
I did question numbers 3 and 5
1. To draw a probability line with a scale in decimals between 0 and 1, you can start by dividing the line into equal segments. Each segment represents a probability value. In this case, you want to place the following events on the line:
a. A person selected at random has a birthday in the summer (June, July, or August).
This event is likely to have a higher probability, so you can place it closer to 1 on the line.
b. A person selected at random has a birthday today.
This event has a very low probability since it only occurs on one specific day, so you can place it closer to 0 on the line.
c. A person selected at random does NOT have a summer birthday.
This event is the complement of event a, so it should be placed at the opposite end of the line, closer to 0.
2. The probability statement "1 in 7 people will win a prize" can be represented as a fraction and a percent.
As a fraction, it is 1/7.
To convert it to a percentage, divide the numerator (1) by the denominator (7) and multiply by 100. This gives (1/7) * 100 = 14.29%. Rounded to two decimal places, the probability is approximately 14.29%.
3. To find the theoretical probability in the bag of marbles, you need to determine the ratios of each marble color.
a. The theoretical probability of getting a blue marble is determined by dividing the number of blue marbles (5) by the total number of marbles (10 + 5 + 3 = 18). So, the probability is 5/18, which is approximately 0.278 when rounded to three decimal places.
b. The theoretical probability that the marble is NOT green can be found by adding the number of red and blue marbles (10 + 5 = 15) and dividing it by the total number of marbles. So, the probability is 15/18, which can be simplified to 5/6.
4. Since the die has 8 faces numbered 1 through 8, the probability of rolling a number greater than 3 can be determined by considering the favorable outcomes (4, 5, 6, 7, and 8) and dividing it by the total number of outcomes (8). So, the probability is 5/8.
To represent it as a percentage, divide the number of favorable outcomes (5) by the total number of outcomes (8), and multiply by 100. This gives (5/8) * 100 = 62.5%. Rounded to one decimal place, the probability is 62.5%.
5. To complete the chart and determine the theoretical probability of rolling the sum of 6 with the pair of four-sided dice, start by listing all the possible outcomes of rolling each die separately:
Die 1: 1, 2, 3, 4
Die 2: 1, 2, 3, 4
Now, list all the sums possible when the dice are rolled together:
1 + 1 = 2
1 + 2 = 3
1 + 3 = 4
1 + 4 = 5
2 + 1 = 3
2 + 2 = 4
2 + 3 = 5
2 + 4 = 6
3 + 1 = 4
3 + 2 = 5
3 + 3 = 6
3 + 4 = 7
4 + 1 = 5
4 + 2 = 6
4 + 3 = 7
4 + 4 = 8
From the chart, we can see that the sum of 6 occurs twice out of the 16 possible outcomes. So, the theoretical probability of rolling the sum of 6 is 2/16, which can be simplified to 1/8.
6. To create a tree diagram for the two spinners, first list all the possible outcomes for each spinner. For example, if spinner 1 has three possible outcomes (red, blue, and green), and spinner 2 has two possible outcomes (yellow and purple), then you would have six possible outcomes for both spinners combined.
Once you have listed the outcomes for each spinner, create a tree diagram with branches connecting the outcomes of the first spinner to the outcomes of the second spinner.
To determine the theoretical probability of getting AT LEAST ONE blue, count the number of outcomes that include a blue from the tree diagram. In this case, there are four outcomes that include a blue (blue-yellow, blue-purple, blue-blue, blue-green) out of the six possible outcomes. So, the theoretical probability of getting at least one blue is 4/6, which can be simplified to 2/3.
7. Without the graphs provided, it is difficult to determine which one is most likely to be correct. Please provide the visuals for accurate assessment.
8. One important concept in probability is the Law of Large Numbers. It states that as the number of trials (or experiments) increases, the experimental probability of an event will approach the theoretical probability. This means that the more times an event is tested or repeated, the closer the observed results will be to the expected results.