Friday

September 19, 2014

September 19, 2014

Posted by **John** on Tuesday, February 19, 2013 at 2:44am.

- Maths -
**n**, Wednesday, February 20, 2013 at 9:16am9

- Maths -
**hehe**, Friday, February 22, 2013 at 9:13pmfail.

- Maths -
**Gwen**, Sunday, February 24, 2013 at 5:23amFirst, we will find the probability of at least one grandchild making consecutive tweets by using the inclusion-exclusion principle, and then subtract the result from 1.

From the inclusion-exclusion principle,

P(at least one grandchild makes consecutive tweets)

= (5 choose 1)P(a specified grandchild makes consecutive tweets) - (5 choose 2)P(two specified grandchildren makes consecutive tweets) + (5 choose 3)P(three specified grandchildren makes consecutive tweets) - (5 choose 4)P(four specified grandchildren makes consecutive tweets) + (5 choose 5)P(all five grandchildren makes consecutive tweets).

For 1 <= k <= 5, we need to find the probability that k specified grandchildren (and possibly others) make consecutive tweets.

There are 10! permutations of all 10 tweets.

Think of arranging k "blocks" of two tweets each, and (10 - 2k) single tweets. There are (10 - k)! ways of arranging these (10 - k) items, and 2 ways of arranging the two tweets within each of the k blocks. So (10 - k)!(2^k) of the 10! permutations result in k specified grandchildren (and possibly others) making consecutive tweets.

So the probability that k specified grandchildren (and possibly others) make consecutive tweets is (2^k)/[10*9*...*(10 - k + 1)].

Therefore, we have

P(at least one grandchild makes consecutive tweets)

= 5(2/10) - 10(4/(10*9)) + 10(8/(10*9*8)) - 5(16/(10*9*8*7)) + 1(32/(10*9*8*7*6))

= 1 - 4/9 + 1/9 - 1/63 + 1/945.

So the probability of no grandchild making consecutive tweets is

1 - (1 - 4/9 + 1/9 - 1/63 + 1/945) = 4/9 - 1/9 + 1/63 - 1/945 = 47/135.

**Answer this Question**

**Related Questions**

Math - Fred is closing a bank account t and wants to distribute the money among...

math - an estate valued at $62,000 is left by a will as follow:to each of two ...

english - I believe that if President Obama and other Democratic leaders run ...

Chemistry - The surface tension versus log concentration for two surfactants is ...

Grammer and capitalization - Select the sentence with the correct capitalization...

English - I believe that if President Obama and other Democratic leaders run ...

maths - The number of arrangements of five letters from the word 'magnetic' that...

math - Be sure to show the calculations that helped in your decision-making. A ...

MAth - A bOY goes on VacATION with fivE shirts.each day HE used TWO diferent ...

Psychology - In organizational psychology, the "Big Five" refers to five general...