# Stuck on a question

#### Dragan8ng

##### New member
So it says there is a 5% of a test being incorrect, so if we try 20 cases what is the probability of it being incorrect less than 3 times?

#### Subhotosh Khan

##### Super Moderator
Staff member
So it says there is a 5% of a test being incorrect, so if we try 20 cases what is the probability of it being incorrect less than 3 times?
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

#### Dragan8ng

##### New member
So the chance of it happening is 1/20 which = 0.05, so to get less than 3 it is 1-0,05 which = 0,95?

#### tkhunny

##### Moderator
Staff member
So the chance of it happening is 1/20 which = 0.05, so to get less than 3 it is 1-0,05 which = 0,95?
Give it another go. Given 20 tests, there is SOME probability that the test will be wrong ALL 20 times! There is also some probability that it will be correct EVERY time.

Given just one test, probabilities are 5% incorrect and 95% correct.
Given two tests, consider (0.05 + 0.95)^2
This should lead you on a trail of discovery.

It would help us help you if you told us up front that you are studying particular material, such as perhaps the Binomial Distribution.

#### Dragan8ng

##### New member
Give it another go. Given 20 tests, there is SOME probability that the test will be wrong ALL 20 times! There is also some probability that it will be correct EVERY time.

Given just one test, probabilities are 5% incorrect and 95% correct.
Given two tests, consider (0.05 + 0.95)^2
This should lead you on a trail of discovery.

It would help us help you if you told us up front that you are studying particular material, such as perhaps the Binomial Distribution.
Doesn't make sense to me, Im studying descriptive statistics, probability, random variables, trust intervals, testing parametrial hypothesis, regression and correlation, linear trend and individual indexes which is part of business statistics

#### Subhotosh Khan

##### Super Moderator
Staff member
So it says there is a 5% of a test being incorrect, so if we try 20 cases what is the probability of it being incorrect less than 3 times?
What is the probability that - out of 20 tests - 0 (none) will be incorrect?

#### Dragan8ng

##### New member
What is the probability that - out of 20 tests - 0 (none) will be incorrect?
That confuses me even more

#### tkhunny

##### Moderator
Staff member
Did you do this? "Given two tests, consider (0.05 + 0.95)^2 "

0.05^2 + 2*0.05*0.95 + 0.95^2

Give a quick read in the Binomial Distribution with p = 0.05 and n = 20.

Is it 0.45?

#### Jomo

##### Elite Member
What do you find so special about 3 to say the probability of it being incorrect less than 3 times is .05?
Would you say the same answer for the probability of it being incorrect less than 2 times?
How about he probability of it being incorrect less than 5 times?
These probabilities can't all be the same. Do you see that?

Do you understand what less than 3 times in this problem?

I will do a part of this problem for you.

p(exactly 2 being incorrect out of 20) = 20C2(.05)2(.95)18 .................... edited

Last edited by a moderator:

#### Jomo

##### Elite Member
Show us your work as I am not going to do the work myself to see if you are correct. I know that you did not mean to be unfriendly but please think about your last post.

#### tkhunny

##### Moderator
Staff member
Please calculate for X = 0, 1, 2. You tell me why.

#### Dragan8ng

##### New member
Please calculate for X = 0, 1, 2. You tell me why.
It's: 0,36, 0,38 and 0,19, so id guess it being less than 3 is the sum of all of those which = 0,93?

#### Jomo

##### Elite Member
It's: 0,36, 0,38 and 0,19, so id guess it being less than 3 is the sum of all of those which = 0,93?
Don't round so much but your numbers are correct.

#### tkhunny

##### Moderator
Staff member
It's: 0,36, 0,38 and 0,19, so id guess it being less than 3 is the sum of all of those which = 0,93?
That's the spirit. Now, listen to Jomo.

• Jomo

#### Subhotosh Khan

##### Super Moderator
Staff member
What do you find so special about 3 to say the probability of it being incorrect less than 3 times is .05?
Would you say the same answer for the probability of it being incorrect less than 2 times?
How about he probability of it being incorrect less than 5 times?
These probabilities can't all be the same. Do you see that?

Do you understand what less than 3 times in this problem?

I will do a part of this problem for you.

p(exactly 2 being incorrect out of 20) = 20C2(.05)2(.95)15
Did you mean to say:

p(exactly 2 being incorrect out of 20) = 20C2(.05)2(.95)18

• Jomo