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

A coin is thrown 3 times .what is the probability that atleast one head  is obtained?

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  least 35 seeds in a bag.

Right Option : B
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Explanation
Question : 3

A coin is tossed 3 times then probability of getting atleast two heads is ___________

Right Option : D
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Explanation
 
 
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