Home
Class 12
MATHS
Numbers are selected at random, one at a...

Numbers are selected at random, one at a time, from the two digit numbers 00,01,02...,99 with replacement. An event `E` occurs if the only product of the two digits of a selected number is 18. If four numbers are selected, find the probability that the event `E` occurs at least 3 times.

Text Solution

Verified by Experts

The correct Answer is:
`(97)/((25)^(4))`
The given numbers are `00,01,02…,99.` There are total 100 numbers, out of which the numbers, the product of whose digits is 18, are `29,36,63,and 92.`
`thereforep=P(E)=(4)/(100)=1/25`
` impliesq=1-p =24/25`
From binomial distribution,
P(E occuring at least 3 times)
=P(E occuring 3 times)+ P (E occuring 4 times)
`=""^(4)C_(3)p^(3)q+""^(4)C_(4)p^(4)`
`=4xx((1)/(25))^(3)((24)/(25))+((1)/(25))^(4)=(97)/((25)^(4))`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY II

    CENGAGE|Exercise Exercise (Single)|68 Videos

  • PROBABILITY II

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • PROBABILITY II

    CENGAGE|Exercise Exercise 14.5|7 Videos

  • PROBABILITY I

    CENGAGE|Exercise JEE Advanced Previous Year|7 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

Similar Questions

Explore conceptually related problems

Numberse are selected at random, one at a time, from the two-digit numbers 00,01,02,….99 with replacement. An event E occurs if and only if the product of the two digits of a selected number is 18. If four numbers are selected, find probability that the event E occurs at least 3 times.

Find the last two digits of the number 3^(600) .

Two integers are selected at random from integers 1 to 11. If the sum is even, find the probability that both the numbers are odd.

A number is selected at random from integers 1 to 100. Find the probability that it is not a perfect cube.

A number is selected from the set {2,3,…,30}. The probability that the selected number is a prime number is

A two digit number is formed with the digits 2,5,9 (repetition is allowed). Find the probability that the number is divisible by 2 or 5 .

The faces of a die bear numbers 0,1,2,3,4,5,. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero.