Home
Class 12
MATHS
Numberse are selected at random, one at ...

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.

Text Solution

Verified by Experts

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

Similar Questions

Explore conceptually related problems

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.

One ticket is selected at random from 100 tickets numbered 00,01,02, …, 99. Suppose A and B are the sum and product of the digit found on the ticket, respectively. Then P((A=7)//(B=0)) is given by

Two integers are selected at random from the set {1, 2, …, 11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is

One ticket is selected at random from 100 tickets numbered 00,01,02,...,98,99. Suppose S and T are the sum and product of the digits of the number on the ticket, then the probability of getting S=9 and T=0 is 2//19 b. 19//100 c. 1//50 d. none of these

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X)

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

Two numbers are selected randomly from the set S={1,2,3,4,5,6} without replacement one by one. The probability that minimum of the two numbers is less than 4 is (a) 1/15 (b) 14/15 (c) 1/5 (d) 4/5