1.) two marbles are drawn without replacement from a bowl containing seven red, four blue, and nine yellow marbles. what is the probability that at least one is red?
2.)a card is drawn from a standard deck of 52 cards. what is the probability that the card is neither a four or a five?
3.)At Studymore University, 46% of students are female and 13% of the female students are psychology majors. 9% of all students are psychology majors. a student is selected at random. what is the probability that the person selected is a female psychology major?
4.)you supervise 12 nurses. in how many ways can you choose four nurses to have the weekend off? what is the probability that four chosen individuals will have the weekend off?
We do not do your work for you. Once you have answered your questions, we will be happy to give you feedback on your work. Although it might require more time and effort, you will learn more if you do your own work. Isn't that why you go to school?
However, I will start you out with the first problem.
1. You are looking for probability of either one red or two reds.
One red = 7/20 * 13/19
Two reds = 7/20 * 6/19
Either-or probability is founds by adding the individual probabilities.
1) To find the probability that at least one marble drawn is red, we need to consider two scenarios: either one red marble is drawn or both marbles drawn are red.
First, let's determine the probability of drawing one red marble. There are a total of 20 marbles in the bowl, and 7 of them are red. So, the probability of drawing one red marble is 7/20 or 0.35.
Next, let's determine the probability of drawing both red marbles. After drawing the first red marble, there will be 6 red marbles left out of the remaining 19 marbles. So, the probability of drawing a second red marble (without replacement) is 6/19 or approximately 0.316.
To calculate the probability of at least one red marble, we can add the probabilities of the two scenarios together:
Probability of one red marble + Probability of both red marbles
= 0.35 + 0.316
= 0.666 or approximately 0.67
Therefore, the probability that at least one marble drawn is red is approximately 0.67.
2) To find the probability that a card drawn is neither a four nor a five, we need to subtract the probability of drawing a four or a five from 1 (since we want the complement event).
There are four fours and four fives in a standard deck of 52 cards. So, the probability of drawing a four or a five is 8/52 or 2/13.
Now, to find the probability of not drawing a four or a five, we can subtract the probability we just calculated from 1:
Probability of neither four nor five = 1 - Probability of four or five
= 1 - (2/13)
= 11/13
Therefore, the probability that a card drawn is neither a four nor a five is 11/13.
3) To find the probability that the randomly selected student is a female psychology major, we need to multiply the probability of being female (46%) by the probability of being a psychology major given that the student is female (13%).
Probability of being a female psychology major = Probability of being female * Probability of being a psychology major given female
= 0.46 * 0.13
= 0.0598 or approximately 0.06
Therefore, the probability that the randomly selected student is a female psychology major is approximately 0.06.
4) To calculate the number of ways to choose four nurses out of twelve to have the weekend off, we can use the combination formula, denoted as C(n, r), where n is the total number of nurses and r is the number of nurses chosen.
The formula for combination is:
C(n, r) = n! / (r!(n-r)!)
In this case, we have 12 nurses and we need to choose 4 nurses, so we have:
C(12, 4) = 12! / (4!(12-4)!)
= 12! / (4! * 8!)
= (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)
= 495
Therefore, there are 495 ways to choose four nurses to have the weekend off.
To find the probability that the four chosen individuals will have the weekend off, we need to compare the number of favorable outcomes (4 nurses having the weekend off) to the total number of possible outcomes (495 ways to choose 4 nurses).
Probability of four nurses having the weekend off = Number of favorable outcomes / Total number of outcomes
= 1 / 495
≈ 0.002
Therefore, the probability that the four chosen individuals will have the weekend off is approximately 0.002 or 0.2%.