Maths Probability Question?

Question

I am really struggling with this simple maths question, my brain has just given up on me, grateful for any help!!! :o)

The probability that a patient will have an allergic reaction to a drug is 0.01, if a group of 15 patients are given the drug what is the probability that 1 patient will have an allergic reaction?

Answer 1

Probability of having a reaction is 0.01
So probability of NOT having a reaction is 0.99 -->from 1-0.01
P(1 person out of 15 will have a reaction)
15*0.01*0.99*0.99*0.99*0.99*0.99*0.99*0.99*0.99*0.99*0.99*0.99*0.99*0.99*0.99
OR
15 * 0.01^1 * 0.99^14
solve this equation

This is because 1 person will have the reaction, and 14 other people will NOT have the reaction
You have to multiply by 15, (it was derived from 15!/1!14!)
because there are 15 ways that this combination could appear.
For example you can have
ABBBBBBBBBBBBBB
or
BABBBBBBBBBBBBB
or
BBABBBBBBBBBBBB
and so on
you need to multiply by 15 to get all the possibilities that this could appear, with one person having a reaction.

Answer 2

This must be confusing for you - there are a lot of different answers here and everyone thinks theirs makes perfect sense.

Intuitively, the answer would be around 15% as Euphojim said. It's only logical, right?

Statistically or mathematically, it doesn't quite work like that. Cccccrazy's answer was the correct answer.
The question asks for the probability that EXACTLY 1 patient has a reaction. This means that 14 patients don't get a reaction.
So the probability that Joe (random patient) gets a reaction is 1% and the probability that Jack, James, and so on don't get a reaction is 99% for each of them.

When you work out probabilities for a number of different things at the same time (like who has a reaction and who doesn't), you multiply the individual probabilities.
This means that the chances of Joe getting sick and noone else is 1%*99%*99%*99%*99%*99%*99%*99%*99%*99%*99%*99%*99%*99%*99%
or
(0.01)^1 * (0.99)^14
= 0.008687

But then the chance that Jack gets sick and everyone else stays the same is 0.008687, and the same for everyone else.

So, for all 15 of them, the total probability is the sum of each individual's probability of getting sick, or:
0.008687 + 0.008687 + 0.008687 + 0.008687 + 0.008687 + 0.008687 + 0.008687 + 0.008687 + 0.008687 + 0.008687 + 0.008687 + 0.008687 + 0.008687 + 0.008687 + 0.008687
= 15 * (0.008687)
= 0.1303
=13.03%

Hope that helps make it clear. When you get into statistics a bit further, you'll see that this is a perfect example of a Binomial Distribution. Then you can just pop the numbers into a formula so it's easier.

Answer 3

I am not a mathematician but if this was supposed to be a simple maths question then surely a simple answer is required.

The 0.01 probability of allergic reaction means that on average 1 in every 100 people will be affected. If there are 15 people then it is 15/100 = 0.15

Answer 4

The probabily that the first person has a reaction and the others do not have is:

0.01 * (0.99)^(14).

The probably that the second person has a reaction and ther others do not have is the same:

0.01 * (0.99)^(14)

and so on...

So the probability that exactly one out of the 15 people having a rxn would be:

15 * 0.01 * 0.99 ^(14)

= 0.1303

Answer 5

ok. we know that the probability of grabbing a red coat on one try is 12/60. 60 because there are a total of 60 coats. the probability of grabbing a yellow coat is 35/60 and so on. there are two ways to solve this. one is first to see that both events (grabbing the first coat) and then (grabbing the second coat) are not independent (that is, if he does not put the coat back after he grabs it). so the probability of grabbing to red coats is 12/60 times 11/59. The second grab is 11/59 because he took one red out which leaves only 11 red coats, and a total of 59 coats. you multiply the two because both events have to occur. In probability if you have 2 events that must occur together you multiply the events. if either can happen, you add them. but back to the problem. the second way to do it is to say there are a total of 60 choose 2 ways to grab any 2 combinatons of coats. the event that he pulls two red coats is 60 choose 12 times 59 choose 11 then divide the whole thing by 60 choose 2. they both should give you the same answer.

Answer 6

0.01 is the common sense....bcoz it hav mentioned tht- a patient will have an allergic reaction to a drug is 0.01.itz a tht means one.
cheers

Answer 7

When you say "1 patient", I assume you mean "at least one patient".

P(at least 1 patient) = 1 - P(exactly no patients)
= 1 - .99^15 = .14

Answer 8

The probability is: 0.01*15= 0.15. That is pure logic.

Answer 9

its 0.01 * (1/15)

Answer 10

Use the binomial probability.

C(15,1)(0.01)(0.99)^14