Probability Q2).
2) A die is so biased that each odd number is twice as likely to occur as each even number.If a die is thrown once find the probability of
i) getting an even no.
ii) getting a number less than 3
iii)getting a prime number

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Solution

Dear Student,

$P r o b a b i l i t y o f g e t t i n g o d d n u m b e r = 2 \times p r o b a b i l i t y o f g e t t i n g e v e n n u m b e r H e n c e l e t P (2) = x, P (4) = x a n d P (6) = x t h e n, P (1) = 2 x, P (3) = 2 x a n d P (5) = 2 x N o w t o t a l p r o b a b i l i t y = 1 h e n c e P (1) + P (2) + P (3) + P (4) + (5) + P (6) = 1 x + x + x + 2 x + 2 x + 2 x = 1 x = \frac{1}{9} i) P r o b a b i l i t y o f g e t t i n g e v e n n u m b e r = P (2 o r 4 o r 6) = P (2) + P (4) + P (6) = \frac{1}{9} + \frac{1}{9} + \frac{1}{9} P r o b a b i l i t y o f g e t t i n g e v e n n u m b e r = \frac{1}{3} i i) p r o b a b i l i t y o f g e t t i n g n u m b e r l e s s t h a n 3 P (1 o r 2) = P (1) + P (2) = x + 2 x = 3 x = 3 \times \frac{1}{9} P (1 o r 2) = \frac{1}{3} i i i) G e t t i n g a p r i m e n u m b e r 2, 3 o r 5 P (2 o r 3 o r 5) = P (2) + P (3) + P (5) = x + 2 x + 2 x = 5 x P (2 o r 3 o r 5) = 5 \times \frac{1}{9} \Rightarrow \frac{5}{9}$
Regards,

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