Q7 of 105 Page 582

A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

From the condition given in the question, it is clear that:

Probability of getting a six in a throw of die =


And, probability of not getting a six =


Let us assume,


Now, we have:


Probability that the 2 sixes come in the first five throws of the die


=


Also, Probability that the six come in the sixth throw




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An urn contains 25 balls of which 10 balls bear a mark 'X' and the remaining 15 bear a mark 'Y'. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability that:

(i) All will bear 'X' mark.


(ii) Not more than 2 will bear 'Y' mark.


(iii) At least one ball will bear 'Y' mark.


(iv) The number of balls with 'X' mark and 'Y' mark will be equal.

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An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.