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?
I will be happy to critique your thinking.
1.) To find the probability of at least one red marble being drawn, we need to calculate the probability of drawing two non-red marbles and subtract it from 1.
First, let's find the probability of drawing two non-red marbles. There are a total of 20 marbles remaining in the bowl (4 blue + 9 yellow + 7 red). When we draw the first marble, there are 20 options, but only 13 of them are non-red. For the second draw, after removing one marble, there are 19 marbles left in the bowl, with 12 of them being non-red.
The probability of drawing two non-red marbles is (13/20) * (12/19) = 156/380.
To find the probability of drawing at least one red marble, subtract this probability from 1:
1 - (156/380) = (380/380) - (156/380) = 224/380 = 28/47.
Therefore, the probability that at least one marble drawn is red is 28/47.
2.) To find the probability that the card drawn is neither a four nor a five, we need to calculate the probability of not drawing any four or five cards.
There are 4 fours and 4 fives in a standard deck of 52 cards. So the total number of cards that are neither fours nor fives is 52 - 4 - 4 = 44.
The probability of drawing a card that is neither a four nor a five is 44/52 = 11/13.
Therefore, the probability that the card drawn is neither a four nor a five is 11/13.
3.) To find the probability of selecting a female psychology major, we need to multiply the probability of selecting a female student by the probability of selecting a psychology major given that the student is female.
The probability of selecting a female student is 46% or 0.46.
The probability of selecting a psychology major given that the student is female is 13% or 0.13.
So, the probability of selecting a female psychology major is 0.46 * 0.13 = 0.0598 or 5.98%.
Therefore, the probability that the person selected is a female psychology major is 5.98%.
4.) To calculate the number of ways to choose four nurses to have the weekend off, we need to use the combination formula.
The combination formula is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of nurses and r is the number of nurses we want to choose.
In this case, n = 12 (the total number of nurses) and r = 4 (the number of nurses to have the weekend off).
Using the combination formula, we can calculate the number of ways to choose four nurses out of twelve:
C(12, 4) = 12! / (4!(12-4)!) = 12! / (4! * 8!) = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1) = 495.
So, there are 495 ways to choose four nurses to have the weekend off.
To find the probability that all four chosen individuals will have the weekend off, we need to calculate the probability of choosing four nurses out of twelve divided by the total number of possible choices.
The total number of possible choices is the total number of ways to choose any four nurses out of twelve:
C(12, 4) = 495.
Therefore, the probability that four chosen individuals will have the weekend off is 495 / 495 = 1 or 100%.