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A number from 1-100 is randomly selected. What is the probability that it is a perfect square, given that it is an odd number?

Respuesta :

mathmate
Events:
1 ≤ n ≤ 100
A=x is a perfect square, i.e. x=n^2
B=x is odd, i.e. n is odd
P(A|B)
=P(A∩B)/P(B)   by definition of conditional probability
(reads Probability that the number is a perfect square given that it is odd)

Since there are 10 perfect squares between 1 to 100 (1,4,9,16,25,36,49,64,81,100), out of which 5 are odd {1,9,25,49,81)
So P(A∩B)=5/100
P(B)=probability of odd x  {1,3,5,7,.....95,97,99}
= 50/100=1/2
Therefore 
P(A|B)=(5/100)/(1/2)=1/10

varshamittal029

The probability that it is a perfect square, given it's an odd number is 0.1

What is conditional probabilty?

The conditional probability of event B is the probability of an event to be occurred in the future with prior knowledge that event A has already occurred.

This is written as P(B|A) is the conditionality probability of B where A has already occurred.

P(B|A)=P(B∩A)/P(A)

Here, B is the event of getting the number as a square number

A is the event of getting the odd number

|A|=50

P(A)= No.of favorable conditions/total no. of objects

=50/100

B∩A is the event of getting a number which square number as well as an odd number

B∩A= { 1,9,25,49,81]

|B∩A|=5

P(B∩A)=No.of favorable condition/total no. of objects

=5/100

So now putting the above values in the formula

P(B|A)=P(B∩A)/P(A)

=(5/100)/(50/100)

=5/50

=1/10

=0.1

Therefore the probability that it is a perfect square, that it is an odd number is 0.1

Learn more about conditionality probability

here: https://brainly.com/question/10739947

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