Two students devised a game called “3 pennies & 2 nickels.” each player will choose to play the pennies or the nickels. in each round, the players will flip all their coins on the table and record how many heads and tails they have. the table below includes the point scheme.

point values for “3 pennies & 2 nickels”
penny points nickel points
all pennies heads: –2 both nickels heads: –2
at least one of each: +3 one of each: +5
all pennies tails: –2 both nickels tails: –2

alyssa wants to play the game. choose the statement below that is correct in all aspects.
e(penny) = –0.33 and e(nickel) = 0.33, so she should play with the nickels.
e(penny) = 0.5 and e(nickel) = 1.5, so she should play with the nickels.
e(penny) = 1.75 and e(nickel) = 1.5, so she should play with the pennies.
e(penny) = 2.38 and e(nickel) = 2, so she should play with the pennies.

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:

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:

B= 8.8

Step-by-step explanation:

B/2 = 4.4

B/2 (2) = 4.4 (2)

B = 8.8