A die with number 1 to 6 is biased such that

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Question 6:- A die with number 1 to 6 is biased such that P(2) = 3/10 and probability of other numbers is equal. Find the mean of the number of times number 2 appears on the dice, if the dice is thrown twice.

Solution:-  Probability of number 2 appears on dice P(A) = 3/10

Probability of number 2 does not appears on dice P(A’) = 1 – 3/10 = 7/10

X = Represent the number 2 appears on dice

X = 0, 1, 2

P(X = 0) = P(A')\times P(A') = \dfrac{7}{10}\times \dfrac{7}{10}

= \dfrac{49}{100}

P(X = 1) = P(A)\times P(A') + P(A')\times P(A)

= \dfrac{3}{10}\times \dfrac{7}{10} + \dfrac{7}{10}\times \dfrac{3}{10}

= \dfrac{21}{100} + \dfrac{21}{100} = \dfrac{42}{100}

P(X = 2) =P(A)\times P(A)

=\dfrac{3}{10}\times \dfrac{3}{10} = \dfrac{9}{100}

X

 0 1 2

P(X)

 49/100 42/100 9/100

Mean = E(x) = 0×49/100 + 1×42/100 + 2×9/100

= 0 + 42/100 + 18/100 = 60/100

= 3/5 = 0.6

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