Question 53 of 55intermediate🔧 ApplyShort Answer3 marks

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: 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?
Correct Answer

The probability that the spokesperson will be either male or over 35 years is 4/5.

Exercise: Miscellaneous Exercise on Chapter 14 | Q: 8 | (Page Page 22)
For More Understanding

Explanation

This question tests the application of the addition theorem of probability: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Students need to identify the favorable outcomes for each event and their intersection, then apply the formula correctly.

Solution Steps

  1. Step 1: Total number of persons = 5

  2. Step 2: Let A = event that person is male. Males are Harish, Rohan, Salim. So P(A) = 3/5

  3. Step 3: Let B = event that person is over 35 years. Persons over 35 are Sheetal (46), Salim (41). So P(B) = 2/5

  4. Step 4: Persons who are both male AND over 35 years = Salim only. So P(A ∩ B) = 1/5

  5. Step 5: Using P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 3/5 + 2/5 - 1/5 = 4/5

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