SOLUTION: in a sample of 1200 adults, 200 dine out more than once a week. 2 adults are selected at random without replacement. Assuming the sample is representative of all adults, what is th

Question 1027044: in a sample of 1200 adults, 200 dine out more than once a week. 2 adults are selected at random without replacement. Assuming the sample is representative of all adults, what is the probability that both adults dine out more than once a week?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
in a sample of 1200 adults, 200 dine out more than once a week. 2 adults are selected at random without replacement. Assuming the sample is representative of all adults, what is the probability that both adults dine out more than once a week?

Solution:
The question requests us to assume that the two adults sample are representative of the population.
So P(dine-out)=200/1200=1/6
For a two step experiment each with a probability of 1/6, the probability of both events succeed is the product, by the multiplication rule, giving
P(both dine-out)=(1/6)(1/6)=1/36=0.02778 (approx.)

In reality, once the first has been sampled, there leaves 199 out-diners out of the 1199 remaining people, so the actual probability is
P(both dine-out)=(1/6)*(199/1199)=199/7194=0.02766 approx.

The last result can also be obtained using the hypergeometric distribution, which is
P(2 successes out of 120)
=C(200,2)C(1000,0)/(1200,2)
=199/7194 as before.

When the population is large, and the probability of success is not extremely low, the specified approximation (of constant probability) is quite close to the exact value, as illustrated by the example.
RELATED QUESTIONS
In a sample of 1200 U.S. adults, 202 dine out at a restaurant more than once per week.... (answered by stanbon)

In a sample of 1100 U.S.�Adults, 198 dine out at a restaurant more than once per... (answered by Gentle Phill)

In a sample of 1200 U.S. adults, 188 dine out at a restaurant more than once per... (answered by Boreal)

In a sample of 800 U.S. adults, 189 dine out at a resaurant more than once per... (answered by Boreal)

In a sample of 80 adults, 28 said that they would buy a car from a friend. Three adults... (answered by ikleyn,rothauserc)

A random sample of 1,750 adults showed that 850 of them have surf the internet at least... (answered by Theo)

There are 1200 adults in a concert.there are 200 more girls than boys how many girls... (answered by rfer)

In a sample of 2016 U.S. adults, 242 said Richard Nixon was the worst president since... (answered by ewatrrr)

. STAYING IN TOUCH- In a poll conducted in 2007, 200 adults ages 18 yr and older were... (answered by edjones)