IIT JEE , AIEEE Forum - Mathematics , Algebra

amway

an unbiased coin is rolled until a number grester than 4 appears on dice .the probability that an even number of tosses are needed is

rhd92781

It shud be "an unbiased dice...".
Probability of getting a no >4, P(E) = 1/3.
Probabiltiy of getting a no<=4, P'(E) = 2/3.
The probability that even no of "rolls" is required = Sum of probabilities that <=4 appears in all turns except an even turn.

=2/3*1/3 + 2/3*2/3*2/3*1/3 + 2/3*2/3*2/3*2/3*2/3*1/3 + ...upto infinity
= 2/9(1 + 4/9 + (4/9)^2 + (4/9)^3 + ...upto infinity)
= 2/9 * 1/(1-4/9)
= 2/9 * 9/5
=2/5

spideyunlimited

prob. that a number greater than 4 appears = 2/6 = 1/3

prob. that a number less than or equal to 4 appears = 2/3

prob. that an even no. of tosses are needed =

(2/3)*1/3 + (2/3)^3*1/3 + (2/3)^5 * 1/3 ......

= 2/9 (1 + (2/3)^2 + (2/3)^4 + (2/3)^6 + ....)

= 2/9 [ 1 / ( 5/9) ]

= (2/9)*(9/5)

= 2/5

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