Probability - E maths

bonkysleuth SG

Hi I have some difficulties trying to understand the following probability questions. Could someone help me out using a tree diagram or any other means for easy interpretation?

In a city, 20% of the citizens are carriers of a certain disease.If a citizen is a carrier, the probabbility that a blood test will indicate a positive result is 0.95. If citizen is a non-carrier, the probability that the blood test will indicate a postive result is 0.10. Two citizens are selected at random for the blood test. Find the probability that

(a) both citizens have positive results

(b) both citizens have negative results

Answers are 0.0729 and 0.5329.

And the following.

There are 6 children - 5 boys and 1 girl in room A, and 9 children - 3 boys and 5 girls in room B. A child from room A is selected at random to move to room B. Then a child from room B is selected at

random for an interview. Find the probability that

(a) the child selected for an interview is a girl.Answer's 37/60.

thanks

maurizio13 SG

If it's very messy like this, it's better to draw out a table, retrieve as much information as possible from it, then evaluate from there.

(0.2 X 0.95 + 0.8 X 0.10) ^2 = (0.27)^2 = 0.0729

You figure out part (b) yourself.

Garrick_3658 SG

There are 6 children - 5 boys and 1 girl in room A, and 9 children - 3 boys and 5 girls in room B. A child from room A is selected at random to move to room B. Then a child from room B is selected at

random for an interview. Find the probability that

(a) the child selected for an interview is a girl.Answer's 37/60.

thanks

6 girls in room B. Is that right?

First instance - If the girl from room A went over to room B, then

probability that the child selected for an interview is a girl = 1/6 x 7/10 = 7/60

Second instance - If the girl from room A DID NOT go over to room B, then

probability that the child selected for an interview is a girl = 5/6 x 6/10 = 1/2

Probability of dependent events = 7/60 + 1/2 = 37/60

Pardon if I sounded alien, but you need some basics knowledge of probability to work this out.

eagle SG

is there a part b for the second question? I would like to add them to ExamWorld... Thanks.

93'guy SG

i love prob . cos the answers wont be more than 1

maurizio13 SG

i love prob . cos the answers wont be more than 1

Even if your answer is wrong, it won't be off by more than 1?

93'guy SG

Even if your answer is wrong, it won't be off by more than 1?

i dont know ~

Garrick_3658 SG

If the probability goes over 1 you know CONFIRM + GUARANTEE wrong liao.