Question

Consider a dice with the property that probability of a face with n dots showing up is proportional to n. Which one of the following is true? Review Later P(3) = 4/21 P(2) = 3/21 P(4) = 4/21 P(1) = 3/21

Answer 1

Answer:

P(3)-4/21 P 2 -3/21P(4)-4/21P(1) -3/21

Answer 2

Given : Consider a dice with the property that probability of a face with n dots showing up is proportional to n.

To Find : Which one of the following is true?  

P(3) = 4/21 P(2) = 3/21 P(4) = 4/21 P(1) = 3/21

Solution:

a face with n dots showing up is proportional to n.

P(1)   ∝   1   => P(1) =  k

P(2) ∝  2 => P(2) = 2k

P(3) ∝ 6  => P(3)  = 3k

P(4) ∝ 6  => P(4)  = 4k

P(5) ∝ 6  => P(5)  = 5k

P(6) ∝ 6  => P(6)  = 6k

Sum of all probabilities = 1

P(1) + P(2) + P(3) + P(4) + P(5) + P(6)  = 1

=> k + 2k + 3k + 4k + 5k + 6k = 1

=> 21k  = 1

=> k = 1/21

P(1) = 1/21

P(2) = 2/21

P(3) = 3/21

P(4) = 4/21

P(5) = 5/21

P(6) = 6/21

Hence in the given options P(4) = 4/21  is correct

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