math

1.Find the number using the following Venn diagram.

n(A ∩ B)

2. Find the number using the following Venn diagram.

n(A ∪ B)

3. Find the number using the following Venn diagram.

n(Ac)

4. Given that n(A) = 20, n(B) = 12, n(A ∩ B) = 8, and n(U) = 38, fill in the four regions in the Venn diagram.

5.

A parking permit sticker displays an identification code consisting of a letter (from A, B, and C) followed by a digit (from 1, 2, and 3). How many different permits can be issued?  permits

6.

The sophomore lacrosse team has 29 players, of whom 10 played defense last year, 14 played offense, and 3 played both defense and offense, while the rest of the players did not play last year. How many members of the team played last year?  players

8.

A computer password is to consist of three alphanumeric characters with no repeats. (An alphanumeric character is a letter from A to Z or a digit from 0 to 9.) How many such passwords are there?  passwords How many are there if the letter O and the digit 0 are excluded to avoid confusion?  passwords

9.

In a town, 36% of the citizens contributed to the Republicans, 46% contributed to the Democrats, and 13% contributed to both. What percentage contributed to neither party?  %

10.

For the game, identify the saddle point and determine the corresponding optimal strategy for each player.

 

5		8
3		7

The saddle point is the  in row  and column  . The optimal strategy is for R to always choose row  and for C to always choose column  .