Math Probability Questions :)

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1) Let x be a random positive integer between 1 and 100 inclusive. Find the probability x leaves a remainder of 4 when divided by 7.

(SOLVED)

2) Let a and b be random reals between 0 and 10 inclusive. Find the probability that a^2+b^2 =< 1 and y >= 1 - x.

 

3) 11 indistinguishable candies are randomly distributed to 4 kids. Find the probability that none of the kids have at most 2 candies.

 

4) Let ab, and c be reals between 10 and -10 inclusive. Find the probability a^2+b^2+c^2 =< 1 and exactly one of the variables ab and c are positive.

5) There are 6 dice numbered with the integers between 0 and 5 inclusive that are fair. Find the probability that when all of the dice are rolled simultaneously, the sum of the numbers shown on the dice is 15. (Its okay to express your answer as binomials, if you do happen to do so, use the form binomial(a, b) where binomial(ab) defines the number of ways to choose a committee of b people from a people.)

 

Thank you,

SuperJupiter5 (Edited username)

Avatar of SuperSaturn
createsure wrote:

1) 13/100

Yes that's correct. It's a pretty trivial question!

Avatar of createsure

LOL, just tried deleting to give others a chance, yes it was easy! Thanks.

Avatar of createsure

5)  21600 out of 46656  (a hair under 46.3%)

(solved non-electronically, except to convert to a percentage)

Avatar of Minecraft710

2) won’t the probability of a^2 + b^2 =< 1 be zero? Both a and b are either 1 or bigger than 1. I don’t know how the y and x inequality is related to a and b though😅. Can anyone help? happy.png

Avatar of createsure
Minecraft710 wrote:

2) won’t the probability of a^2 + b^2 =< 1 be zero? Both a and b are either 1 or bigger than 1. I don’t know how the y and x inequality is related to a and b though😅. Can anyone help?

no, I had the exact same thought... the first part is zero, and WTH is the second part even talking about? LOL. It's like part of the problem is missing or something.

Avatar of This_Is_Amazing

1) 7/50 (4,11,18,25,32,39,46,53,60,67,74,81,88,95)

if u divide 7 into 4 the remainder is 4 

Avatar of xdd1200

The answer of (2) should be (pi - 2)/400

Avatar of createsure

3) The answer is zero probability. Either that or I don't understand the wording. I take it to mean that NONE of the kids have 2, 1, or zero candies. In other words, everyone must have at least 3. Which is not possible, hence zero probability.

Avatar of This_Is_Amazing

dude its randomized

 

Avatar of This_Is_Amazing

a possible configuration can be 1,1,1,8

 

Avatar of createsure
This_Is_Amazing wrote:

a possible configuration can be 1,1,1,8

 

What does the phrase "at most" mean then? The first kid has 1 candy in your example. Does he have "at most 2 candies"? Yes, he does. 

So, we can pretend that the question says "none of them have 2 candies" which would be a fairly easy problem to work out. But that is NOT what it says. Just as the phrase "at least" means that number or more, the phrase "at most" means that number or less. And 1 is less than 2, so your example is invalid.  

Avatar of thomas31408

4, 0

Avatar of thomas31408

I mean for 3, 0