Consider a die that has been designed such that all even numbers are equally likely, all odd numbers are equally likely, but an even number is twice as likely as an odd number. what is the probability that this die lands 2?

  2/n where n is the number of faces on the die

A 6-sided die could be numbered 1, 2, 2, 3, 4, 4 to meet the probability requirements 2/6 = 1/3 of the faces have the number 2, so the probability of 2 would be 1/3.

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To meet the probability requirements nicely requires a die with a number of faces that is a multiple of 3. The regular solids meeting this requirement are

A dodecahedron could be numbered 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4 and the probability of a 2 would be the same as for a cube. It could more reasonably be numbered 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, in which case, the probability of 2 would be 1/6.

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If you use some other shape or put blank faces on the die (say a 20-faced die with 2 blanks), then the probability will be different from the numbers above. If you still use 2 faces for each even number, then the probability of 2 using an n-faced die is 2/n.

the line of

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%