Finite Homework: Probability and statistics.

Question

1. Assume that there are 19 frozen dinners: 10 pasta, 6 chicken, and 3 seafood dinners. The student selects 5 of them.

What is the probability that at least 2 of the dinners selected are pasta dinners?

 

2. Assume that there are 6 different issues of Sports Illustrated, 7 different issues of Newsweek, and 4 different issues of Popular Science, including the December 1st issue, on the rack. You choose 4 of them at random.

What is the probability that you choose at least 1 of the Newsweek magazines?

 

3. Assume that the playbook contains 9 passing plays and 16 running plays. The coach randomly selects 9 plays from the playbook.

What is the probability that the coach selects at least 3 passing plays and at least 3 running plays?

Answer 1

Katie,

       I'll outline how to do problem 1. the other two are very similar.

 

19  Frozen dinners

10  Pasta

  6  Chicken

  3  Seafood

 

Select 5 at random find p(that at least 2 are pasta}

 

we have 10 pasta and 9 not pasta

First calculate the number of combinations of 2 pastas      ₁₀C₂ =45 no. of non pasta ₉C₃ =84

So the total number of combinations having 2 pastas is 45*84=3780

     the  total number                        having 3 pastas is 120*36=4320

doing the same calculation for 4 and 5 pastas and adding them up gives 10,242 combinations having 2,3,4 or5 pastas

 

The  total number of combinations of 5 out of 19 is ₁₉C₅=11,628

So p(of at least 2 pastas)=10,242/11,628=.881.

Could have calculated the probability of 0 and  1 pastas and subtracted it form one...fewer calculations

 

Jim