At the Most Probability


 
 
Concept Explanation
 

At the Most Probability

At The Most Probability:

 In general language at the most means that the set can have value less than or equal to that value. For example in a bag of balls numbered 1 to 20, the ball having number at the most 10 means a group of balls having value less than or equal to 10. At most in the probability means that the favorable cases are those possibilities that that are smaller than or equal to that value. So, we can say that at most means maximum value the group can have.

Illustration: Fifty seeds were selected at random from each of 5 bags of seeds, and were kept under standarised conditions favorable to germination. After 20 days the number of seeds which had germinated in each collection were counted and recorded as follows:

Bag: 1 2 3 4 5
Number of seeds germinated: 40 48 42 39 41

What is the probability of germination of:

(i) more than 40 seeds is a bag?       

Solution:Total number of bags = 5

Bags in which more than 40 seeds germinated out of 50 seeds are 2, 3, and 5

So total number of bags in which more than 40 seeds germinated out of 50 seeds = 3

large therefore     Probability of germination of more than 40 seeds in a bag

 P(E)= frac{Number ;of;favourable ;bags}{Total;bags}= frac{3}{5}

(ii) at most 40 seeds in a bag?

Solution:Total number of bags = 5

Bags in which at most 40 seeds germinated out of 50 seeds are 1 and 4

So total number of bags in which at most 40 seeds germinated out of 50 seeds = 2

large therefore     Probability of germination of at most 40 seeds in a bag

 P(E)= frac{Number ;of;favourable ;bags}{Total;bags}= frac{2}{5}

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Sample Questions
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Question : 1

Fifty seeds were selected at random from each of 5 bags of seeds, and were kept under standardised conditions favourable to germination. After 20 days, the number of seeds, which had germinated was counted and recorded as follows :

Bag 1 2 3 4 5
No. of seeds germinated 40 26 42 39 41

What is the probability of germination of at most 40 seeds in a bag.

Right Option : A
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Explanation
Question : 2

Fifty seeds were selected at random from each of 5 bags of seeds, and were kept under standardised conditions favourable to germination. After 20 days, the number of seeds, which had germinated was counted and recorded as follows :

Bag 1 2 3 4 5
No. of seeds germinated 34 26 30 39 41

What is the probability of germination of at most 30 seeds in a bag.

Right Option : B
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Explanation
Question : 3

Over the past 200 working days, the number of defective parts produced by a machine is given in the following table:

Number of defective parts 0 1 2 3 4 5 6 7 8
Days 28 32 22 18 12 12 10 10 10

Determine the probability that tomorrows output will have:at most one defective part.

Right Option : B
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Explanation
 
 
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