Let S be the sample space of all five-digit n | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The total number of $5$-digit numbers is $n(S) = 9 	imes 10^4 = 90000$.Let $A$ be the set of numbers that are multiples of $7$ but not divisible

Vedclass · Accepted Answer

$1.0285$

Vedclass · Answer

(C) The total number of $5$-digit numbers is $n(S) = 9 	imes 10^4 = 90000$.Let $A$ be the set of numbers that are multiples of $7$ but not divisible by $5$.Smallest $5$-digit number divisible by $7$ is $10003$.Largest $5$-digit number divisible by $7$ is $99995$.Using the formula $a_n = a + (n-1)d$,we have $99995 = 10003 + (n-1)7$,which gives $n = 12857$.Now,find numbers divisible by both $7$ and $5$,i.e.,divisible by $35$.Smallest $5$-digit number divisible by $35$ is $10010$.Largest $5$-digit number divisible by $35$ is $99995$.$99995 = 10010 + (P-1)35$,which gives $P = 2572$.The number of elements in $A$ is $12857 - 2572 = 10285$.The probability $p = \frac{10285}{90000}$.Therefore,$9p = 9 	imes \frac{10285}{90000} = \frac{10285}{10000} = 1.0285$.

Let $S$ be the sample space of all five-digit numbers. If $p$ is the probability that a randomly selected number from $S$ is a multiple of $7$ but not divisible by $5$,then $9p$ is equal to.

Similar Questions

There are $5$ horses in a race. Mr. $A$ selects $2$ horses at random and bets on them. What is the probability that the winning horse is among the horses selected by Mr. $A$ (in $/5$)?

An integer $x$ is chosen at random from $1$ to $50$. The probability that $x + \frac{336}{x} \leq 50$ is

$A$ card is selected from a pack of $52$ cards. Calculate the probability that the card is an ace of spades.

If $P(A \cup B)=0.8$ and $P(A \cap B)=0.3$, then $P(\bar{A})+P(\bar{B})$ is equal to:

The probability of happening an event $A$ is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events,then the probability of happening neither $A$ nor $B$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module