Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram’s selection is 1/6 and that of Ramesh is 1/8. What is the probability that only one of them will be selected?
1/4
In this problem, we are asked to find the probability that only one of the two candidates, Ram and Ramesh, will be selected for a job interview. We are given their individual probabilities of selection.
Probability of Only One Selection in an Interview
To solve this, we need to consider two distinct situations where only one person gets selected, and then sum their probabilities. First, let's list the given probabilities and calculate the probabilities of non-selection.
Ram and Ramesh Probabilities
We are provided with the following probabilities for Ram's selection and Ramesh's selection:
- Probability of Ram's selection, \( P(R) = \frac{1}{6} \).
- Probability of Ramesh's selection, \( P(M) = \frac{1}{8} \).
Now, we need to find the probability that each candidate is not selected. The probability of an event not occurring is \(1\) minus the probability of the event occurring.
- Probability of Ram not being selected, \( P(R') = 1 - P(R) = 1 - \frac{1}{6} = \frac{6}{6} - \frac{1}{6} = \frac{5}{6} \).
- Probability of Ramesh not being selected, \( P(M') = 1 - P(M) = 1 - \frac{1}{8} = \frac{8}{8} - \frac{1}{8} = \frac{7}{8} \).
Selection Scenarios for One Candidate
The problem asks for the probability that only one of them will be selected. This can happen in two mutually exclusive ways:
- Ram is selected, AND Ramesh is NOT selected.
- Ramesh is selected, AND Ram is NOT selected.
We will calculate the probability for each of these selection scenarios.
Scenario 1: Ram is Selected and Ramesh is Not Selected
Since the selection events are independent, we multiply their individual probabilities:
\( P(\text{Ram selected and Ramesh not selected}) = P(R) \times P(M') \)
\( = \frac{1}{6} \times \frac{7}{8} \)
\( = \frac{1 \times 7}{6 \times 8} \)
\( = \frac{7}{48} \)
Scenario 2: Ramesh is Selected and Ram is Not Selected
Similarly, for this scenario, we multiply their individual probabilities:
\( P(\text{Ramesh selected and Ram not selected}) = P(M) \times P(R') \)
\( = \frac{1}{8} \times \frac{5}{6} \)
\( = \frac{1 \times 5}{8 \times 6} \)
\( = \frac{5}{48} \)
One Person Probability Calculation
To find the total probability that only one of them will be selected, we add the probabilities of these two mutually exclusive scenarios:
\( P(\text{Only one selected}) = P(\text{Ram selected and Ramesh not selected}) + P(\text{Ramesh selected and Ram not selected}) \)
\( = \frac{7}{48} + \frac{5}{48} \)
\( = \frac{7 + 5}{48} \)
\( = \frac{12}{48} \)
Finally, we simplify the fraction:
\( = \frac{12 \div 12}{48 \div 12} \)
\( = \frac{1}{4} \)
Thus, the probability that only one of Ram or Ramesh will be selected is \( \frac{1}{4} \).
Important Questions from Numerical Computation
Ratio of the angles of a triangle are 1 : 2 : 6. What is the smallest angle?
It would take one machine 4 hours to complete a production order and another machine 2 hour to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is ________ hours.
Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD_remaining in the budget.
What is the value of \(1 + \frac{1}{4} + \frac{1}{{16}} + \frac{1}{{64}} + \frac{1}{{256}} + \ldots ?\)
A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?
