If two events are independent, the probability of both events occurring is the product of their individual probability. Events A and B are independent with P(A)=0.3 and P(B)=0.25 . What is the probability of events A and B happening at the same time? Write your answer in decimal form.
Bot GPT 3.5
answered
P(A and B) = P(A) * P(B) = 0.3 * 0.25 = 0.075
So, the probability of events A and B happening at the same time is 0.075 in decimal form.
A person
answered
Studying Online
Girls Boys Row total
Want the option to keep studying online 10 3 13
Don’t want the option to keep studying online 5 7 12
Column total 15 10 25What is the probability of selecting a student who wants the option to keep studying online? Write your answer in percent form.
Bot GPT 3.5
answered
The total number of students in the sample is 25.
So, the probability of selecting a student who wants the option to keep studying online is:
P(student wants to keep studying online) = Number of students who want to keep studying online / Total number of students
P(student wants to keep studying online) = 13 / 25 = 0.52
Converting this to percentage form: 0.52 * 100% = 52%
Therefore, the probability of selecting a student who wants the option to keep studying online is 52% in percent form.
A person
answered
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items
Question
A money envelope contains five $10 bills, ten $20 bills, and fifteen $50 bills. Sandra randomly selects two bills without returning the first bill. What is the probability of getting a $10 bill then a $50 bill? Write your answer in the simplest form of fraction.
Bot GPT 3.5
answered
Total number of bills = 5 (from $10 bills) + 10 (from $20 bills) + 15 (from $50 bills) = 30 bills
Total number of outcomes when selecting two bills = 30 * 29 (she doesn't return the first bill) = 870 outcomes
The number of ways to get a $10 bill and then a $50 bill can be calculated as:
Number of ways to get a $10 bill = 5 (from $10 bills)
Number of ways to get a $50 bill = 15 (from $50 bills)
Therefore, the total number of ways to get a $10 bill followed by a $50 bill = 5 * 15 = 75 ways
The probability of this happening is the number of favorable outcomes (getting a $10 bill followed by a $50 bill) divided by the total number of outcomes:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 75 / 870
Probability = 15 / 174
Therefore, the probability of getting a $10 bill followed by a $50 bill is 15/174 in the simplest form of a fraction.
A person
answered
Bot GPT 3.5
answered
The total number of bills = 5 (from $10 bills) + 10 (from $20 bills) + 15 (from $50 bills) = 30 bills
When Sandra selects the first bill, the total number of bills decreases by 1, so the total number of outcomes for her second selection would be 30 - 1 = 29.
The number of ways to get a $10 bill on the first draw is 5.
The number of ways to get a $50 bill on the second draw, given that the $10 bill was selected first, is 15.
Therefore, the total number of ways to get a $10 bill followed by a $50 bill is 5 * 15 = 75 ways.
So the probability of selecting a $10 bill then a $50 bill is:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 75 / (30 * 29)
Probability = 75 / 870
Probability = 5 / 58
Therefore, the probability of getting a $10 bill then a $50 bill is 5/58.
