Kenneth Rosen Edition 7 Exercise 7.2 Example 2 (Page No. 455)

Question

Why is it 7 in the denominator?

Comments

because all number appears once and 3 appear twice :)

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$\frac{1}{x} + \frac{1}{x} + \frac{1}{x} + \frac{1}{x} + \frac{1}{x} +\frac{2}{x} = 1$

$\Rightarrow x = 7$

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@just_bhavna @srestha

Why is it not as follows?
= 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 2/6

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let probability of {1,2,4,5,6} = p

probability of {3} = 2p

since total sum of probability = 1

p+p+p+p+p+2p = 1

p=1/7

Prob{1,2,4,5,6} = p =1/7

prob{3} = 2p = 2/7

prob(odd)=prob(1,5,3) = 1/7 + 1/7 + 2/7 = 4/7.

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@manu because sum of total probabilities is 1

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thanks bhavna!

Answer 1

It is given "3 appears twice as often as each other number". We can say from this statement

{1},{2},{4},{5},{6} are equally likely events therefore P(1) = P(2) = P(4) =P(5) =P(6) = (say,x)

while probability of event {3} = 2x

Sum of all probabilities = 1 = 2x + 5x

x = 1/7 Therefore P(1) = P(2) = P(4) =P(5) =P(6) = 1/7  while P(3) = 2/7

Probability that an odd number appears = P(1) + P(3) + P(5) = 1/7 + 2/7 + 1/7 = 4/7