Question

A positive integer is picked randomly from 41 to 50, inclusive.

What is the probability that it is divisible by either 3 or 5? Write your answer as a simplified fraction

Answer 1

again we count
only ten numbers to count
41,42,43,44,45,46,47,48,49,50
then we count the ones divisible by 3, and the ones divisible by 5

Answer 2

All integers are divisible by 3 or 5. What I think you meant is divisible by 3 or 5 without a remainder right?

Answer 3

divisible by 3: 42,45,48
divisible by 5: 45,50

just make sure not to count 45 twice (the whole point of this problem) so the set is
{42,45,48,50} i.e 4 out of the 10

Answer 4

ya commodoc that is implied

Answer 5

so these events are not mutually exclusive and we apply the concept of union ?

Answer 6

well they are not mutually exclusive that is for sure, since 45 is both divisible by 3 and by 5

Answer 7

i am not sure what you mean by "concept of union" you would take the union of the two events in any case, whether they are mutually exclusive or not

Answer 8

but what is the concept of union and intersection in probability

Answer 9

commdoc u can also try

Answer 10

unions and intersections are set operations. so for the example above if A is "divisible by 3" and B is "divisible by 5" then
\[A=\{42,45,48\}\]
\[B=\{45,50\}\]
\[A\cup B=\{42,45,48,50\}\]
\[A\cap B=\{45\}\]

Answer 11

and you can see that
\[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]

Answer 12

so in union ever item is considered and in intersection only the common item is taken

Answer 13

hey commdoc u r doing which subject in ur ph.d?

Answer 14

ee
with concentration in communications specifically coding theory

Answer 15

Hey satellite how do you get the drawings in the blog?