I have a couple of tasks that I'm struggling with. I think I got the first three correct, but I'm entirely stuck on the last ones. BTW thanks for looking at my topic and any help will be appreciated. Sorry if this post contains bad English or explanations.
Question 1 is: There are 5 red balls and 3 blue balls in a box. We are going to pick up 4 of them randomly. What is the probability that;
A: We end up with 4 red
B: we end up with 3 red and 1 blue
C: we end up with two of each
The answer I got on that task is (BTW I got the calculations, done, I just don't know how to write it here).
A: 0.07142
B:0.4285
C:0.4285
Question 2 is: A political party has 30% of a population on their side. We are picking out 20 people randomly out of the whole population. What are the odds that
A: 5 of them are followers of the mentioned political party
B: 6 of them are
C: 7 of them are
The answers I got here are
A:0.14573
B:0.18214
C:0.18213
Task 3: 40% of the students at a school have mathematics as a subject, 25% have biology and 15% have both.
A: decide P(B|M)
B: decide P(M|B)
where B=biology and M=math
Answers I got, don't know if they're correct.
A:0.6... 0.15/0.25
B:0.375.... 0.15/0.4
Task 4 Two schools are participating in a competition/lottery. they are picking one random student from one of the schools. First they do a coin toss to decide which school they pick from.
At one of the schools there are 55% boys and at the other there are 40% boys. What is the probability that a boy wins the lottery?
the answer I got on this one is 0.475. (0.5*0.55)+(0.5*0.4)
Task 5: We have two boxes. Box one has 2 white balls and 2 green balls. Box 2 has 5 white balls and 3 green balls. If you do a coin toss to decide which one you pick from.
A: What is the probability that you pick up a green ball?
B: You picked a green ball in a experiment like this, what is the probability that the ball came from box one?
Edit: I tried this on task A: (0.5*0.5)+(0.5*0.375)=0.4375
I'm entirely stuck on this one after a couple of hours with lots of failed calculations. I may have got A right but I got a lot of different answers. No idea about B
Task 6: A factory is producing a product. Assume that 99.5% of the products are functional=0.5% are defect. When they test the product there is a 95% probability that the test will show if a defect product is defect.
And if an item is functional there is a 97% probability that the test will show that it is functional.
Question A:if the test shows the product to be defect, what is the probability that it is actually functional?
B: if the test shows that the product is functional, what is the probability that it's actually defect?
Have been stuck on this one as well for hours.
And lastly is a tough one.
There are two coins in a box. One of them is normal and the other one has coin on both sides. Lets say that you pick one coin from the box randomly and do a coin toss 3 times. Assume that you got coin on all the 3 tosses. what is the
probability that you used the normal coin?
I don't even know where to start on that one.
Thanks a lot to anyone who decides to help me out. Sorry if the text contains bad English. It's my third language. If I explained some of the tasks bad, please let me know.
Question 1 is: There are 5 red balls and 3 blue balls in a box. We are going to pick up 4 of them randomly. What is the probability that;
A: We end up with 4 red
B: we end up with 3 red and 1 blue
C: we end up with two of each
The answer I got on that task is (BTW I got the calculations, done, I just don't know how to write it here).
A: 0.07142
B:0.4285
C:0.4285
Question 2 is: A political party has 30% of a population on their side. We are picking out 20 people randomly out of the whole population. What are the odds that
A: 5 of them are followers of the mentioned political party
B: 6 of them are
C: 7 of them are
The answers I got here are
A:0.14573
B:0.18214
C:0.18213
Task 3: 40% of the students at a school have mathematics as a subject, 25% have biology and 15% have both.
A: decide P(B|M)
B: decide P(M|B)
where B=biology and M=math
Answers I got, don't know if they're correct.
A:0.6... 0.15/0.25
B:0.375.... 0.15/0.4
Task 4 Two schools are participating in a competition/lottery. they are picking one random student from one of the schools. First they do a coin toss to decide which school they pick from.
At one of the schools there are 55% boys and at the other there are 40% boys. What is the probability that a boy wins the lottery?
the answer I got on this one is 0.475. (0.5*0.55)+(0.5*0.4)
Task 5: We have two boxes. Box one has 2 white balls and 2 green balls. Box 2 has 5 white balls and 3 green balls. If you do a coin toss to decide which one you pick from.
A: What is the probability that you pick up a green ball?
B: You picked a green ball in a experiment like this, what is the probability that the ball came from box one?
Edit: I tried this on task A: (0.5*0.5)+(0.5*0.375)=0.4375
I'm entirely stuck on this one after a couple of hours with lots of failed calculations. I may have got A right but I got a lot of different answers. No idea about B
Task 6: A factory is producing a product. Assume that 99.5% of the products are functional=0.5% are defect. When they test the product there is a 95% probability that the test will show if a defect product is defect.
And if an item is functional there is a 97% probability that the test will show that it is functional.
Question A:if the test shows the product to be defect, what is the probability that it is actually functional?
B: if the test shows that the product is functional, what is the probability that it's actually defect?
Have been stuck on this one as well for hours.
And lastly is a tough one.
There are two coins in a box. One of them is normal and the other one has coin on both sides. Lets say that you pick one coin from the box randomly and do a coin toss 3 times. Assume that you got coin on all the 3 tosses. what is the
probability that you used the normal coin?
I don't even know where to start on that one.
Thanks a lot to anyone who decides to help me out. Sorry if the text contains bad English. It's my third language. If I explained some of the tasks bad, please let me know.
