R = the number of racks

s = the number of shoes

Which of the variables is independent and which is dependent?

number of shoes is independent, number of racks is dependent

Step-by-step explanation:

the number of racks does not affect the number of shoes but if there are a lot of shoes, the number of racks will increase.

E(penny)=1.75 and E(nickel)=1.5 , so she should play with the pennies.

Step-by-step explanation:

We are given Point Values for “3 Pennies & 2 Nickels” as:

Penny Points                             Nickel Points

All pennies heads: –2        Both nickels heads: –2

At least one of each: +3One of each: +5

All pennies tails: –2         Both nickels tails: –2

Since, the outcome of 3 pennies are given as:

{HHH,TTT,HTH,THH,HHT,HTT,THT,TTH}=8 outcomes.

Now the probability of all head=1/8

         ( since the outcome is HHH)

          Similarly,

Probability of at least one of each= 6/8

          ( since the outcomes are HTH,THH,HHT,HTT,THT,TTH)

and probability of all pennies tail = 1/8

            ( Since the outcome is TTT)

Now the outcome of 2 nickel is given as:

{HH,HT,TH,TT}

So, the probability of both nickel head =1/4

             ( Since, we have the outcome as HH)

Probability of one of each= 2/4

              ( Since, the outcome is HT,TH)

Probability of both nickels tail= 1/4

                ( since, the outcome is TT)

Now, Expectation is calculated as sum of the terms obtained by the  product of outcomes and it's probability.

E(penny) is calculated as:

Similarly, E(nickel) is calculated as: