X is the number of times the dial lands on region A. Which table represents the probability distribution for the variable X?

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1 Answer
Apr 16, 2018

#P(0)=4/9#, #P(1)=4/9# and #P(2)=1/9#

Explanation:

Please refer to this question.

We have #P(0)=q^2#, #P(1)=2pq# and #P(2)=p^2#

note that #P(1)# is twice the geometric mean of #P(0)# and #P(2)#. Also sum of all probabilities is #q^2+2pq+p^2=(q+p)^2=1#

As this is true only in second case (top right) with #P(0)=4/9#, #P(1)=4/9# and #P(2)=1/9#

Note in first and third case they do not add up to #1#, while in fourth #P(1)# is not twice the geometric mean of #P(0)# and #P(2)#.