Introduction about Probability:

 It is useful for finding the number of occurrence of event in the possible outcomes. Probability lies between 0 and 1.

P(A)=0 means that the event cannot occur, such a probability is called zero probability.

P(A)=1 means the event can occur.

Types of probability

Single event Probability

Multiple events Probability

 

 

Problems on zero probability:

 

Example 1:

A die is tossed once. What the probability of get the number 7.

Solution:

If die is tossed once, the total number of occurrence S= {1, 2, 3, 4, 5, 6} and, therefore, n(S) =6

To getting the number 7.

Number of occurrence for getting the number 7 is zero

n(A)= 0, because when a die is tossed. We have a number from 1 to 6. There is no chance to get a number 7. Such a probability is called zero probability.

Example 2:

            Two coins are tossed once. What the probability of getting three heads.

Solution:

If two coins are tossed once, the total number of occurrence S= {HH,HT,TH,TT} and, therefore, n(S) =4

Number of occurrence for getting three heads is zero

n(A)= 0, because when two coins are tossed. We have getting maximum of two heads. There is no chance to get three head at once. Such a probability is called zero probability

 

 

Example 3:

A die is tossed once. What the probability of get the number greater than 6.

Solution:

If die is tossed once, the total number of occurrence S= {1, 2, 3, 4, 5, 6} and, therefore, n(S) =6

Number of occurrence for getting the number greater than 6 is zero

n(A)= 0, because when a die is tossed. We have a number from 1 to 6. There is no chance to get a number is greater than 6. Such a probability is called zero probability.

 

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Problem 4:

If two dies are rolled what is probability of getting sum of 15 numbers?

Solution:

If two die is rolled the total number of occurrences are,

S =       {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

             (2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

            (3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

            (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

            (5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

            (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

            So there are 36 occurrences

            Probability of getting sums 15 is not possible. Because maximum possible is 6+6 =12

Such a probability is called Zero probability