Question

1. A study of a disease reveals that there is an average of 1 case every 22 square miles. Residents of a town that has an area of 10 square miles are concerned because there are two cases in their area. The state’s Department of Health has decided to investigate further if the probability of getting two or more cases in this town is less than 0.05. Does the Department of Health investigate further?   (3)

2. A lottery is carried out by choosing five balls, without replacement, from a box of 35 balls. The lottery ticket has five numbers on it. Find the probability that exactly four of the balls that come out of the box match the numbers on the lottery ticket. (3)

3. A neighborhood has 32 households – 27 white, and 5 nonwhite. A subset of 9 of these households move to an adjacent neighborhood. What is the probability that less than two of the households in the new neighborhood are nonwhite? (3)

Answer 1

Answer:

Given that:

1)  A study of a disease reveals that there is an average of 1 case every 22 square miles. Residents of a town that has an area of 10 square miles are concerned because there are two cases in their area.

average case= 1 every 22 square miles

= 1/22 every squsre mile

= (1/22) * 10 every 10 square mile

=0.4545 every 10 square mile

Let X be the number of cases in the town

X~ Poisson ( 0.4545)

P( Two or more cases)

= P( X >=2)

= 1 - P( X <2)

= 1 -0.92327

= 0.07673

As the probability is not less than 0.05, so Department should not investigate furthur.

2)  A lottery is carried out by choosing five balls, without replacement, from a box of 35 balls. The lottery ticket has five numbers on it.

Total number of balls = 35

5 numbers match the lottery ticket and remaining 35 are different

P( exactly 4 of the balls that come out of the box match the number on the lottery ticket)