And OR Conditions in Probability


 
 
Concept Explanation
 

And OR Conditions in Probability

And Or Conditions in Probability:

In general language And means that if both the conditions is true only then the result is true, whereas in the case of Or if any one of the condition is true then the result is true. In probability,  And means that the outcome has to satisfy both conditions at the same time. Or means that the outcome has to satisfy one condition, or the other condition, or both at the same time.

For example while drawing a ball from a bag of balls having 1 to 50 numbered balls

The favorable cases for getting a ball having a number divisible by 3 and 5. The favorable cases will be balls having number 15, 30, and 45 because only these number satisfy the conditions that number divisible by 3 and 5.

Whereas The favorable cases for getting a ball having a number divisible by 3 or 5. The favorable cases will be

Balls having number 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48 = 16

As all these numbers are divisible by 3 and

Balls having number 5, 10, 15, 20, 25, 30, 35, 40, 45, 50  =10

As all these numbers are divisible by 5

but we have to exclude the cases in which the number are divisible by both 3 and 5 that is 15, 30 and 45 = 3

As these numbers have appeared in the list of both cases

So the total number of favorable cases are = Favorable cases for numbers divisible by 3 + Favorable cases for numbers divisible by 5 - Favorable cases for numbers divisible by 3 and 5

                                                                              = 16 + 10 - 3

                                                                             = 26 - 3 = 23

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Sample Questions
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Question : 1

In a pack of card , numbered 1 to 150, how many numbers are divisible by both 10 or 7 ?

Right Option : A
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Question : 2

What is the probability that a card randomly from a well - shuffled pack of cards is a red king ?

Right Option : B
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Explanation
Question : 3

A card is drawn from a pack of well - shuffled cards. what is the probability of getting a king or an ace ?

Right Option : B
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Explanation
 
 
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