QuestionCalculate the expected value of winnings with payouts $2, 3, 4, 5, 6$ and probabilities $0.40, 0.20, 0.17, 0.13, 0.10$ . Round to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions1. The payout amounts are $,$ 3, $4,$ 5, and $6. The corresponding probabilities are0.40,0.20,0.17,0.13, and0.10 respectively3. The expected value is calculated as the sum of the product of each payout and its corresponding probability

STEP 2

The formula for expected value is given by $(X) = \sum (x_i \cdot p_i)$ where $x_i$ is the payout and $p_i$ is the corresponding probability.

STEP 3

Now, plug in the given values for the payouts and their corresponding probabilities into the formula.
$(X) = (2 \cdot0.40) + (3 \cdot0.20) + ( \cdot0.17) + (5 \cdot0.13) + (6 \cdot0.10)$

STEP 4

Calculate the product of each payout and its corresponding probability.
$(X) =0.80 +0.60 +0.68 +0.65 +0.60$

STEP 5

Add up all the values to find the expected value.
$(X) =0.80 +0.60 +0.68 +0.65 +0.60 =3.33$ The expected value of the winnings from the game is $3.33. However, we are asked to round to the nearest hundredth.

STEP 6

Rounding $3.33$ to the nearest hundredth gives $3.33$ .
So, the expected value of the winnings from the game is $3.33.

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QuestionCalculate the expected value of winnings with payouts $2, 3, 4, 5, 6$ and probabilities $0.40, 0.20, 0.17, 0.13, 0.10$ . Round to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions1. The payout amounts are $,$ 3, $4,$ 5, and $6. The corresponding probabilities are0.40,0.20,0.17,0.13, and0.10 respectively3. The expected value is calculated as the sum of the product of each payout and its corresponding probability

STEP 2

The formula for expected value is given by $(X) = \sum (x_i \cdot p_i)$ where $x_i$ is the payout and $p_i$ is the corresponding probability.

STEP 3

Now, plug in the given values for the payouts and their corresponding probabilities into the formula.
$(X) = (2 \cdot0.40) + (3 \cdot0.20) + ( \cdot0.17) + (5 \cdot0.13) + (6 \cdot0.10)$

STEP 4

Calculate the product of each payout and its corresponding probability.
$(X) =0.80 +0.60 +0.68 +0.65 +0.60$

STEP 5

Add up all the values to find the expected value.
$(X) =0.80 +0.60 +0.68 +0.65 +0.60 =3.33$ The expected value of the winnings from the game is $3.33. However, we are asked to round to the nearest hundredth.

STEP 6

Rounding $3.33$ to the nearest hundredth gives $3.33$ .
So, the expected value of the winnings from the game is $3.33.

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QuestionCalculate the expected value of winnings with payouts 2,3,4,5,62, 3, 4, 5, 62,3,4,5,6 and probabilities 0.40,0.20,0.17,0.13,0.100.40, 0.20, 0.17, 0.13, 0.100.40,0.20,0.17,0.13,0.10. Round to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions1. The payout amounts are ,, ,3, 4,4, 4,5, and $6. The corresponding probabilities are0.40,0.20,0.17,0.13, and0.10 respectively3. The expected value is calculated as the sum of the product of each payout and its corresponding probability

STEP 2

The formula for expected value is given by(X)=∑(xi⋅pi)(X) = \sum (x_i \cdot p_i)(X)=∑(xi​⋅pi​)where xix_ixi​ is the payout and pip_ipi​ is the corresponding probability.

STEP 3

Now, plug in the given values for the payouts and their corresponding probabilities into the formula.(X)=(2⋅0.40)+(3⋅0.20)+(⋅0.17)+(5⋅0.13)+(6⋅0.10)(X) = (2 \cdot0.40) + (3 \cdot0.20) + ( \cdot0.17) + (5 \cdot0.13) + (6 \cdot0.10)(X)=(2⋅0.40)+(3⋅0.20)+(⋅0.17)+(5⋅0.13)+(6⋅0.10)

STEP 4

Calculate the product of each payout and its corresponding probability.(X)=0.80+0.60+0.68+0.65+0.60(X) =0.80 +0.60 +0.68 +0.65 +0.60(X)=0.80+0.60+0.68+0.65+0.60

STEP 5

Add up all the values to find the expected value.(X)=0.80+0.60+0.68+0.65+0.60=3.33(X) =0.80 +0.60 +0.68 +0.65 +0.60 =3.33(X)=0.80+0.60+0.68+0.65+0.60=3.33The expected value of the winnings from the game is $3.33. However, we are asked to round to the nearest hundredth.

STEP 6

Rounding 3.333.333.33 to the nearest hundredth gives 3.333.333.33.So, the expected value of the winnings from the game is $3.33.

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QuestionCalculate the expected value of winnings with payouts $2, 3, 4, 5, 6$ and probabilities $0.40, 0.20, 0.17, 0.13, 0.10$ . Round to the nearest hundredth.

Assumptions1. The payout amounts are $,$ 3, $4,$ 5, and $6. The corresponding probabilities are0.40,0.20,0.17,0.13, and0.10 respectively3. The expected value is calculated as the sum of the product of each payout and its corresponding probability

The formula for expected value is given by $(X) = \sum (x_i \cdot p_i)$ where $x_i$ is the payout and $p_i$ is the corresponding probability.

Now, plug in the given values for the payouts and their corresponding probabilities into the formula.
$(X) = (2 \cdot0.40) + (3 \cdot0.20) + ( \cdot0.17) + (5 \cdot0.13) + (6 \cdot0.10)$

Calculate the product of each payout and its corresponding probability.
$(X) =0.80 +0.60 +0.68 +0.65 +0.60$

Add up all the values to find the expected value.
$(X) =0.80 +0.60 +0.68 +0.65 +0.60 =3.33$ The expected value of the winnings from the game is $3.33. However, we are asked to round to the nearest hundredth.

Rounding $3.33$ to the nearest hundredth gives $3.33$ .
So, the expected value of the winnings from the game is $3.33.