Question

According to a report by the Commerce Department in the fall of 2004, 20% of U.S. households had some type of high-speed Internet connection. Let N_n denote the number of U.S. households with a high-speed Internet connection in n households. What is the probability that 20 of the first 200 households surveyed have high-speed Internet given that 5 of the first 75 households surveyed have it?

Answer 1

We need to find the probability of 20 households out of 200 households having high speed internet when 5 of the first 75 households already have a high speed internet.

So basically Nn should be 20 and n is given 200.

Now since 5 out of first 75 households have high speed internet so basically we need to find the probability that of the rest

(200 - 75) = 125 households there should be (20-5) households having high speed internet.

So basically 15 households out of 125 should have high speed internet.

Now number of ways in which 15 households can be chosen out of 125 households is ¹²⁵C₁₅.

And given to us the probability of a household having high speed internet is 0.2 so probability of not having the high internet connection is 0.8

So required probability of 15 households having high internet is 0.2¹⁵   and that of rest 110 not having high internet is 0.8¹¹⁰ .

So the total probability required is ¹²⁵C₁₅ * 0.2¹⁵ *0.8¹¹⁰ = 6.4969 * 10^-3

So the required answer is 6.4969 * 10^-3 .

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