The experimental probability of a simple event is P(event) = number of times an event occurs: total number of trials
EXAMPLE: The following line plot shows the students’ birthdays in a class. Compare the theoretical and experimental probability.
Based on the data from the class, experimental P(Tuesday) = 5/25=1/5=0.2=20%
Because there are 7 days in a week, theoretical P(Tuesday) = 1/7=0.14=14%
Please complete the following question:
In experiment, a coin is flipped 30 times and the results are
{H, H, H, T, T, T, T, H, T, H, H, T, H, H, H, T, T, H, H, H, T, H, T, T, H, T, H, H, H, H}.
Heads: 18
Tails: 12
(2 points)
Round your answer to the tenth place (one digit).
Determine the experimental P(head) =
.
To calculate the experimental probability of landing heads on the coin flip experiment, we can use the formula:
P(head) = number of times heads occurs / total number of trials
In this case, the number of times heads occurred is 18, and the total number of trials is 30.
Therefore, the experimental probability of landing heads is:
P(head) = 18 / 30 = 0.6
So, the experimental probability of landing heads is 0.6 or 60%.
Determine the theoretical P(head) =
The theoretical probability of landing heads on a fair coin is 0.5. Therefore, the theoretical probability of landing heads in this experiment is 0.5 or 50%.
One hundred students were asked about their favorite subject. The results are:
Science Math Art PE Others
Number of students: 15, 10, 30, 30, 15
If 200 more students are asked the same question, how many of them would you expect to like mathematics?
(1 point)
Responses
10%
10%
1/10
1 tenth
2
2
20
To find the probability of a student liking mathematics, we need to look at the number of students who like math compared to the total number of students surveyed.
Number of students who like math: 10
Total number of students surveyed: 100
Probability of liking math = Number of students who like math / Total number of students surveyed
Probability of liking math = 10 / 100
Probability of liking math = 0.10 or 10%
If 200 more students are asked the same question, and the probability of liking math is 10%, then the number of students we would expect to like math out of the additional 200 students can be calculated as:
Expected number of students liking math out of additional 200 students = 0.10 * 200
Expected number of students liking math out of additional 200 students = 20
Therefore, we would expect 20 out of the additional 200 students asked to like mathematics.
Use the table to answer the question.
Number of White Balls selected Number of red balls selected
Bowl A: 5 15
Bowl B: 16 14
Bowls A and B contain a number of white and red balls. Simon repeatedly selected a ball from both bowls and recorded the results in a table. If there are 36 balls in Bowl A, estimate the number of white balls based on Simon’s results.
(1 point)
Responses
9
9
10
10
18
18
27
To estimate the number of white balls in Bowl A, we can use the experimental probability approach.
From the results provided, Simon selected balls from Bowl A and Bowl B.
For Bowl A:
Number of white balls selected = 5
Number of red balls selected = 15
Total number of balls selected from Bowl A = 5 + 15 = 20
Let's calculate the experimental probability of selecting a white ball from Bowl A:
Experimental Probability of selecting a white ball from Bowl A = Number of white balls selected / Total number of balls selected from Bowl A
Experimental Probability of selecting a white ball from Bowl A = 5 / 20 = 0.25
Since experiments are conducted to estimate the probability based on observed outcomes, we can use this experimental probability to estimate the number of white balls in Bowl A.
If there are 36 balls in Bowl A, we can estimate the number of white balls by multiplying the total number of balls in Bowl A by the experimental probability of selecting a white ball:
Estimated number of white balls in Bowl A = Total number of balls in Bowl A * Experimental Probability of selecting a white ball
Estimated number of white balls in Bowl A = 36 * 0.25
Estimated number of white balls in Bowl A = 9
Therefore, the estimated number of white balls in Bowl A based on Simon's results is 9.
Bob spun a spinner with 6 equal sections 150 times and recorded the results. Based on the data which outcomes are equally likely?
Data:
Color and frequency
Blue, 20
red, 15
green, 45
yellow, 10
black, 15
white, 45
(1 point)
Responses
red and blue
red and blue
red and green
red and green
red and yellow
red and yellow
red and black
red and black
red and white
In order for two outcomes to be equally likely, they must have the same probability of occurring. The probability of an event occurring can be calculated by:
Probability of an event = Number of times the event occurred / Total number of trials
Based on the data provided by Bob's 150 spins, we can calculate the probability of each color:
Probability of blue = 20 / 150 = 1/7.5 ≈ 0.1333
Probability of red = 15 / 150 = 1/10 = 0.1
Probability of green = 45 / 150 = 1/3 = 0.3333
Probability of yellow = 10 / 150 = 1/15 ≈ 0.0667
Probability of black = 15 / 150 = 1/10 = 0.1
Probability of white = 45 / 150 = 1/3 = 0.3333
Comparing the probabilities calculated, we can see that the pairs of outcomes that are equally likely are:
- Red and green
- Red and white
Therefore, the correct response is:
red and green
Which equation is equivalent to 11x−(2−x)=51
?
(1 point)
Responses
13x=51
13 x is equal to 51
12x=53
12 x is equal to 53
12x=49
12 x is equal to 49
10x=53
10 x is equal to 53