An integer is chosen at random from the integers 1, 2, 3, ..., 50. The probability that the chosen integer is a multiple of at least one of 4, 6, and 7 is

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
An integer is chosen at random from the integers 1, 2, 3, ..., 50. The probability that the chosen integer is a multiple of at least one of 4, 6, and 7 is [2024]

1 $\frac{8}{25}$

2 $\frac{9}{50}$

3 $\frac{14}{25}$

4 $\frac{21}{50}$

Ans.
(4)

Let A, B, C be the events represents the numbers divisible by 4, 6 and 7 respectively.

$∴$ $n (A) = 12, n (B) = 8, n (C) = 7$

$n (A \cap B) = 4, n (B \cap C) = 1, n (A \cap C) = 1$

$and n (A \cap B \cap C) = 0$

$So, n (A \cup B \cup C) = 12 + 8 + 7 - 4 - 1 - 1 = 21$

$∴$ $Required probability = \frac{21}{50}$

Want Us to Email you About Special Offers & Updates?