an integer is chosen at random between between 1 and 100 find the probability that it is divisible by 8 and not divisible by 8
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Answered by
820
Number of integers between 1 and 100 : 2, 3 , 4, 5 , .....99
so, sample space { or total outcomes } = 98
So, you can say total number of sample space , n(S) = 98
Now , numbers , which are divisible by 8 are : 8 , 16 , 24 , 32, 40 , 48 , 56, 64, 72 , 80, 88 , 96
So, total number which are divisible by 8 = 12
So, number of possible event , n(E ) = 12
Now, probability that it is divisible by 8 , P(E) = n(E)/n(S) = 12/98 = 6/49
P(divisible by 8) = 6/49
Probability that it is not divisible by 8 , P(E') = 1 - probability that is is divisible by 8,P(E)
E.g., P( not divisible by 8) = 1 - 6/49 = (49 - 6)/49 = 43/49
so, sample space { or total outcomes } = 98
So, you can say total number of sample space , n(S) = 98
Now , numbers , which are divisible by 8 are : 8 , 16 , 24 , 32, 40 , 48 , 56, 64, 72 , 80, 88 , 96
So, total number which are divisible by 8 = 12
So, number of possible event , n(E ) = 12
Now, probability that it is divisible by 8 , P(E) = n(E)/n(S) = 12/98 = 6/49
P(divisible by 8) = 6/49
Probability that it is not divisible by 8 , P(E') = 1 - probability that is is divisible by 8,P(E)
E.g., P( not divisible by 8) = 1 - 6/49 = (49 - 6)/49 = 43/49
deepu081003:
did you read the question properly
it says between 1 and 100
It says an integer is chosen randomly between 1 and 100. So, you should include 1 and 100 too . Read answer properly
In questions there is integer between 1 and 100 not 1 to 100 so the sample space is 98 not hundred according to your explanation
I beg to differ from your answer
The sample space should be 98 as' randomly' just suggests that there is equal chance for any number to be selected and 'between' does not include the ends
1-3/25 =22/25 and not 23/25
But where is 23/25
Exactly true the sample spaces will be 98.... Even ncert support it
Is your answer right??? Please tell me...
Answered by
190
Given:
- An integer is chosen between 1 and 100.
- Numbers that are divisible by 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 and 96.
- The rest are not divisible by 8.
Calculation:
The integers are 2, 3, 4, 5, 6,..., 99.
The number of possible outcomes = 98 (Excluding 1 and 100)
Therefore,
Sample space, n(S) = 98.
So,
The possibility of the number divisible by 8, n(E) = 12.
To find probability,
By formula,
P(E) = n(E)/n(S)
=12/98
= 6/49
Hence, P(integer divisible by 8) = 6/49
To find the possibility of the number not divisible by 8,
Probability of an integer it is not divisible by 8,
By formula,
P(E') = 1 - P(E)
1 - 6/49 = (49 - 6)/49
Hence, P(integer not divisible by 8) = 43/49
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