Home
Class 12
MATHS
The unbiased dice is tossed until a numb...

The unbiased dice is tossed until a number greater than 4 appear. What is the probability that an even number of tosses is needed?

Text Solution

Verified by Experts

According to the question, number greater than 4 may appear in `2^(nd),4^(th),6^(th),...` trial. Probability of getting number greater than 4 in any trial `=2/6=1/3`
`therefore` Probability of not getting the number greater than 4 in any trial `=1-1/3=2/3` Let A, be the evetn the number greater than 4 occurs in the trial. Now, result of each trial is independent of earlier trials. So, required probability
`=P(A_(1)'nnA_(2))+P(A_(1)'nnA_(2)'nnA_(3)'nnA_(4)'nnA_(5)'nnA_(6))+...`
`P(A_(1)')P(A_(2))P(A_(1)')P(A_(2)')P(A_(3)')P(A_(4))+...`
`=2/3xx1/3+2/3xx2/3xx1/3+2/3xx2/3xx2/3xx2/3xx2/3xx1/3+...`
`(2/3xx1/3)/(1-2/3xx2/3)("Sun of infinite G.P.")`
`=2/5`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES|21 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise CONCEPT APPCICATION EXERCISE 14.1|5 Videos

  • PROBABILITY I

    CENGAGE PUBLICATION|Exercise JEE Advanced|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE )|8 Videos

Similar Questions

Explore conceptually related problems

The probability distrubution of the number of successes in two tosses of a die where a success is defined as getting a number greater than 4 then the probability distribution of number of successes in two tosses of are die are

Two unbiased dice are thrown. What is the probability that the sum of the numbers on the dice is 9?

A man throws a die until he gets a number greater than 3 . The probability that he gets 5 in the last throw

A fair coin is tossed until one of the two sides occurs twice in a row. The probability that the number of tosses required is even is

Suppose we throw a die once. (1) What is the probability of getting a number greater than 4? (in) What is the probability of getting a number less than or equal to 4?

A biased coin with probability p(0 lt plt 1) of falling tails is tossed until a tail appears for the first time. If the probability that tail comes in odd number of trials is (2)/(3) , then p equals

There unbiased dice are thrown at a time . What is the probability that the number 1 appears at lest once? Given that the number on the first die is 3. What is the probability that the sum of the numbers on the three dice is odd?

An unbiased coin is tossed three times in succession. What is the probability of obtaining 'Tail' at least once ?

In 10 independent throws of a defective die, the probability that an even number will appear 5 times is twice the probability that an even number will appear 4 times. Find the probability that an even number will not apper at all in 10 independent throws of the die.

Two dice thrown simultaneously. What is the probability that the first dice give even number and sum of two numbers is 8?