NCERT Class XI Mathematics - Probability - Solutions
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Question : 53
Total: 54
From the employees of a company, 5 persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows :
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?
| S.No. | Name | Sex | Age in years |
|---|---|---|---|
| 1. | Harish | M | 30 |
| 2. | Rohan | M | 33 |
| 3. | Sheetal | F | 46 |
| 4. | Alis | F | 28 |
| 5. | Salim | M | 41 |
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?
Solution:
Here, total number of persons = 5
One spokesperson is selected out of 5 persons in
C 1
Let E be the event that a person is male and F be the event that a person is over 35 years.
There are 3 males and one person can be selected in
C 1
∴ P (E) =
There are 2 persons who are over 35 years. So, one person can be selected in
C 1
∴ P (F) =
There is 1 person who is male and over 35 years.
∴ P (E ∩ F) =
Now, P(either male or over 35 years) = P(E ∪ F) = P(E) + P(F) – P(E ∩ F)
=
+
−
One spokesperson is selected out of 5 persons in
Let E be the event that a person is male and F be the event that a person is over 35 years.
There are 3 males and one person can be selected in
∴ P (E) =
There are 2 persons who are over 35 years. So, one person can be selected in
∴ P (F) =
There is 1 person who is male and over 35 years.
∴ P (E ∩ F) =
Now, P(either male or over 35 years) = P(E ∪ F) = P(E) + P(F) – P(E ∩ F)
=
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