# Probability question help (1 Viewer)

#### mgg20

##### New Member
Hi,
I would appreciate if someone could help me with a question that I need the answer to before Sunday (10th may?)
I have tried for so long to answer this questions but I truly do not know how. I don’t even know/understand what parts to calculate and how to do it. I’m really struggling here.

1) weather forecasts are generally right, but not always. For a particular winter, the local forecast predicts rain for 35% of day’s and rain occurs on 38% of days. For 25% of winter days, rain was forecast and rain does fall.
a) for what percentage of days does it rain without rain being forecast?
b) what is the probability that there was no rain forecast nor did it rain?
c) on what percentage of days were there either rain or rain forecast?
d) if it is raining, what is the probability that rain was forecast?
e) are rain and forecast for rain mutually exclusive events) explain
f) are rain and forecast for rain independent events? Explain.

#### ultra908

##### Active Member
if you want, you can pretend there are 100 days in this winter so percentages dont get confusing. This q is actually like just one big venn diagram. The question says- on 35 days, it is forecast to rain. It actually rains on 38 days. On 25 days, it is both forecast to rain and it actually it rains.

a. If on 25% of days (i.e 25 days) rain falls when it is forecast, and on 38% (38) of days it rains, the no of days it rains without forecast is 38-25=13 days.
b. If it rains on 38% of days, it doesnt rain 62% of days. It is forecast to rain on 35% of days, but it only rains when forecast 25% of days. Thus 10% of days it is forecast but doesnt rain. Therefore 52% of days it isnt forecast and doesnt rain.
c. It rains when forecast- 25%. It rains but not forecast- 13%. It forecast but not rain- 10%. Thus 48%.
d. Ok imagine there r 100 days. It rains 38% or 38 days. If it is raining, it is one of these 38 days. Now of these 38 days, 25 days it is forecast to rain. So probability is 25/38.
e. Mutually exclusive means cant occur at the same time- can rain and rain forecast occur at the same time?
f. Does the occurence of rain affect the rain forecast? What about the other way around?

Last edited:
• mgg20 and Velocifire

#### Velocifire

##### Out of Order
Do you have to, I was trying to do it strictly using 30, 31, 31. Cause I get half days when I calculate percentages. I just think it seems more practical? Since rain can stop here and there normally.

• mgg20

#### mgg20

##### New Member
if you want, you can pretend there are 100 days in this winter so percentages dont get confusing. This q is actually like just one big venn diagram. The question says- on 35 days, it is forecast to rain. It actually rains on 38 days. On 25 days, it is both forecast to rain and it actually it rains.

a. If on 25% of days (i.e 25 days) rain falls when it is forecast, and on 38% (38) of days it rains, the no of days it rains without forecast is 38-25=13 days.
b. If it rains on 38% of days, it doesnt rain 72% of days. It is forecast to rain on 35% of days, but it only rains when forecast 25% of days. Thus 10% of days it is forecast but doesnt rain. Therefore 62% of days it isnt forecast and doesnt rain.
c. It rains when forecast- 25%. It rains but not forecast- 13%. It forecast but not rain- 10%. Thus 48%.
d. Ok imagine there r 100 days. It rains 38% or 38 days. If it is raining, it is one of these 38 days. Now of these 38 days, 25 days it is forecast to rain. So probability is 25/38.
e. Mutually exclusive means cant occur at the same time- can rain and rain forecast occur at the same time?
f. Does the occurence of rain affect the rain forecast? What about the other way around?
Thank you very much!

• ultra908

#### ultra908

##### Active Member
Do you have to, I was trying to do it strictly using 30, 31, 31. Cause I get half days when I calculate percentages. I just think it seems more practical? Since rain can stop here and there normally.
ye like u said its just more practical. It doesn't tell you how many days the winter is, and the percentages and probabilities don't change dependent on how many days the winter has, u can make it a convenient number like 100.

#### mgg20

##### New Member
I was wondering if someone could help me with another question? this one has really confused me, and unfortunately is worth 14 marks.

Q: Wildlife biologists inspect 157 deer taken by hunters and find 33 of them carrying ticks that test positive for lyme disease. Previous data indicates that the percentage of deer carrying such ticks is 25%.

Is there significant evidence that the percentage of deer carrying ticks that test positive for lyme disease has decreased?
a) write appropriate hypotheses
b) check the assumption and conditions
c) perform the hypothesis test and fine the P-value
d) state your conclusion in plain english. Use a significance level of 5%
e) construct a 90% confidence interval for the true percentage of deer that carry the ticks, and comment on your interval in relation to your conclusion from part d).

Thank you very much for the help!

#### CM_Tutor

##### Moderator
Moderator
if you want, you can pretend there are 100 days in this winter so percentages dont get confusing. This q is actually like just one big venn diagram. The question says- on 35 days, it is forecast to rain. It actually rains on 38 days. On 25 days, it is both forecast to rain and it actually it rains.

a. If on 25% of days (i.e 25 days) rain falls when it is forecast, and on 38% (38) of days it rains, the no of days it rains without forecast is 38-25=13 days.
b. If it rains on 38% of days, it doesnt rain 72% of days. It is forecast to rain on 35% of days, but it only rains when forecast 25% of days. Thus 10% of days it is forecast but doesnt rain. Therefore 62% of days it isnt forecast and doesnt rain.
c. It rains when forecast- 25%. It rains but not forecast- 13%. It forecast but not rain- 10%. Thus 48%.
d. Ok imagine there r 100 days. It rains 38% or 38 days. If it is raining, it is one of these 38 days. Now of these 38 days, 25 days it is forecast to rain. So probability is 25/38.
e. Mutually exclusive means cant occur at the same time- can rain and rain forecast occur at the same time?
f. Does the occurence of rain affect the rain forecast? What about the other way around?
Might need to check if any of these calculations are wrong because "If it rains on 38% of days, it doesnt rain 72% of days" adds up to 110% of days...

#### ultra908

##### Active Member
Might need to check if any of these calculations are wrong because "If it rains on 38% of days, it doesnt rain 72% of days" adds up to 110% of days...
tyty fixed. Imma make these mistakes in exams • CM_Tutor