Atleast Probability


 
 
Concept Explanation
 

At Least Probability

At Least Probability:

 In general language at least means that the set can have value more than or equal to that value. For example in a bag of balls numbered 1 to 20, the ball having number at least10 means a group of balls having value more than or equal to 10. At least in the probability means that the favorable cases are those possibilities that that are larger than or equal to that value. So, we can say that at least means minimum value the group can have.

Illustration: The percentage of marks obtained by a student in monthly unit tests are given below.

Test I II III IV V VI
Percentage of marks 52 60 65 75 80 72

Find the probability that in the next test the student gets:

(i) more than 70% marks

Solution:Total number of tests = 6

The tests in which the student scored more than 70% marks are IV, V and VI

Number of tests in which the student scored more than 70% marks = 3

large therefore  P (more than 70% marks)

 P(E)= frac{Number ;of;favourable ;Tests}{Total;tests}= frac{3}{6}=frac{1}{2}

(ii) at least 60% marks

Solution:Total number of tests = 6

 The tests in which the student scored at least 60% marks  are II, III, IV, V, VI

Number of tests in which the student scored at least 60% marks = 5

P(E)= frac{Number ;of;favourable ;Tests}{Total;tests}= frac{5}{6}

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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 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 at least 40 seeds in a bag?

Right Option : D
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Question : 2

The percentage of marks obtained by Shubham in 3 monthly unit test are: 1st-60, 2nd-58, 3rd-61 (60,58 and 61 are in %). Based on this data the probability that Shubham gets at least 60% marks in a unit test is:

Right Option : B
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Explanation
Question : 3

The score of a batsman in 80 ODI's is as follows:

Score   20 - 29  30 - 30 40 - 49  50 - 59  60 - 69 70 -79 80-89 90-99
Number of matches 1 1 8 13 20 22 12 3

What is the probability that in the next match the batsman will score at least 70 runs?

Right Option : C
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Explanation
 
 
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