1.A garage has a letter-keypad lock with thetenletters A,B,C,D,E,F,G,H,I,J.

The keypad can be programmed with a 4 or 5-letter code to open the garage.

a)Suppose each letter can be used more than once, how many 4-letter codes are possible if:the same letter is not repeated four times?

b)If each letter cannot be repeated, how many 5-letter codes are possible if:

the letter "E" cannot be used?

2.In a group of34employees,14 take public transitwhile12 drive to work.

10 employeesfrom this group are to be selected for a study.

Note: Employees either only take the public transit, only drive to work, or do neither.

How many of the possible groups of 10 employees will:

a)consist of at least one person that takes public transit?

b)consist of at least one person that drives to work?

3.SupposeXhas a binomial distribution withn=11andp=0.69

X=0,1,2,...,11

. Determine the following probabilities. Use software. Rounding is not necessary. If you must round, keep at least 4 decimal places.

a)P(X=6.9)=

b)P(X>6.9)=

c)P(6X11)=

4.The probability distribution of a discrete random variableX

is given below.

x 0 1 2 3 4 5

P(X) 0.20 ?? 0.20 0.14 0.08 0.34

Determine the indicated probabilities. Round to 3 decimal places where necessary to round.

a)P(X2)=

b)P(1X<5)=

c)P(X2 or X3)=

d)P(X1 and X>3)=

e)P(0.5X5.9)=