I have 2 questions that i need help on, please help! Thank you and God bless you.
1. A shoebox holds a number of disks of the same size. There are 5 red, 6 white, and 7 blue disks. You pick out a disk, record its color, and return it to the box. If you repeat this process 250 times, how many times can you except to pick either a red or white disk?
2. Each student in a class of 25 students in a class of 25 students wrote down a random digit. What is the predicted number of students who wrote a digit greater than 7?
You have 18 discs in the box of which 11 are red or white,
so the prob(red or white) = 11/18
Since you are returning the disc, that prob remains the same
So in 250 turns, how many times do you think your event will happen ?
2nd, not enough data. There are an infinite number of numbers greater than 7
Was there a restriction on the numbers they could pick?
there are only two digits greater than 7 -- 8 and 9
so, I'd expect 2/10 of the students to have chosen one of them.
1. To find out how many times you can expect to pick either a red or white disk, we can calculate the probability of picking a red or white disk on each trial and then multiply it by the total number of trials.
The probability of picking a red or white disk on each trial is the sum of the probabilities of picking a red disk and picking a white disk.
The probability of picking a red disk is 5 (number of red disks) divided by the total number of disks (5 red + 6 white + 7 blue = 18). So the probability of picking a red disk is 5/18.
Similarly, the probability of picking a white disk is 6 (number of white disks) divided by the total number of disks (18), so the probability of picking a white disk is 6/18.
Therefore, the probability of picking either a red or white disk on each trial is (5/18) + (6/18) = 11/18.
To find out how many times you can expect to pick either a red or white disk in 250 trials, you can multiply the probability by the number of trials:
Expected number of times picking either a red or white disk = Probability of picking either a red or white disk * Number of trials
= (11/18) * 250
= 154.17 (rounded to the nearest whole number)
Therefore, you can expect to pick either a red or white disk around 154 times.
2. To find the predicted number of students who wrote a digit greater than 7, we need to calculate the probability of each student writing a digit greater than 7 and then multiply it by the total number of students.
Since each student wrote down a random digit, the probability of any particular student writing a digit greater than 7 is 3/10, because there are 3 digits (8, 9, 10) greater than 7 out of the total 10 digits (0-9).
Therefore, the predicted number of students who wrote a digit greater than 7 can be calculated by multiplying the probability by the total number of students:
Predicted number of students who wrote a digit greater than 7 = Probability of a student writing a digit greater than 7 * Total number of students
= (3/10) * 25
= 7.5 (rounded to the nearest whole number)
Therefore, the predicted number of students who wrote a digit greater than 7 is 8.
Of course, I would be happy to help you with your questions! Here's how you can find the answers:
1. To calculate the number of times you can expect to pick either a red or white disk, you need to first determine the probability of picking either a red or white disk on a single pick.
To do this, you can add up the number of red and white disks, which gives you a total of 5 + 6 = 11 disks.
The probability of picking either a red or white disk is then the number of red and white disks divided by the total number of disks: 11 / (5 + 6 + 7) = 11 / 18. This represents the probability of picking a red or white disk on a single pick.
Next, you multiply the probability of picking a red or white disk on a single pick by the total number of picks you make, which is 250. So, the expected number of times you can expect to pick either a red or white disk would be: (11 / 18) * 250.
You can compute this value by multiplying 11/18 by 250, and that will give you the final answer.
2. To find the predicted number of students who wrote a digit greater than 7, you need to determine the probability of writing a digit greater than 7 for a single student.
Since each student wrote down a random digit, we can assume that any digit from 0 to 9 is equally likely to be chosen.
Out of these 10 possible digits, only 8, 9 are greater than 7. Therefore, the probability of a student writing a digit greater than 7 is 2/10 or 1/5.
To find the predicted number of students who wrote a digit greater than 7, you multiply the probability (1/5) by the total number of students in the class (25). So, the predicted number of students who wrote a digit greater than 7 would be: (1/5) * 25.
You can find this value by multiplying 1/5 by 25, and that will give you the final answer.
I hope this helps you find the answers to your questions! Let me know if you need further assistance.