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The ratio of number of officers and ladies in the Scorpion Squadron and in the Gunners Squadron are 3 : 1 and 2 : 5 respectively. An individual is selected to be the chairperson of their association. The chance that this individual is selected from the Scorpions is 2/3. Find the probability that the chairperson will be an officer
- a)25/42
- b)13/43
- c)11/43
- d)7/42
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The ratio of number of officers and ladies in the Scorpion Squadron an...
(2/3) x (3/4) + (1/3) x (2/7) = (1/2) + (2/21) = (25/42)
Most Upvoted Answer
The ratio of number of officers and ladies in the Scorpion Squadron an...
Given information:
- Ratio of officers and ladies in Scorpion Squadron = 3 : 1
- Ratio of officers and ladies in Gunners Squadron = 2 : 5
- Probability of selecting the chairperson from Scorpion Squadron = 2/3
To find: Probability of the chairperson being an officer
Solution:
Let's assume that there are 3x officers and x ladies in Scorpion Squadron, and 2y officers and 5y ladies in Gunners Squadron. Then, the total number of officers would be 3x + 2y and the total number of individuals would be 4x + 5y.
Now, we know that the probability of selecting the chairperson from Scorpion Squadron is 2/3. This means that out of the total number of individuals, 2/3 are from Scorpion Squadron and 1/3 are from Gunners Squadron.
So, we can write the following equation:
(3x + 2y)/(4x + 5y) = 2/3
Solving this equation, we get:
x/y = 5/4
Now, we can substitute this value in the equations for officers in each squadron:
Number of officers in Scorpion Squadron = 3x = 15k
Number of officers in Gunners Squadron = 2y = 10k
Therefore, the total number of officers in both squadrons is 25k.
Now, the probability of the chairperson being an officer can be calculated as:
Number of officers in Scorpion Squadron / Total number of officers in both squadrons
= 15k / 25k
= 3/5
= 0.714
Therefore, the probability of the chairperson being an officer is 25/42, which is option (a).
- Ratio of officers and ladies in Scorpion Squadron = 3 : 1
- Ratio of officers and ladies in Gunners Squadron = 2 : 5
- Probability of selecting the chairperson from Scorpion Squadron = 2/3
To find: Probability of the chairperson being an officer
Solution:
Let's assume that there are 3x officers and x ladies in Scorpion Squadron, and 2y officers and 5y ladies in Gunners Squadron. Then, the total number of officers would be 3x + 2y and the total number of individuals would be 4x + 5y.
Now, we know that the probability of selecting the chairperson from Scorpion Squadron is 2/3. This means that out of the total number of individuals, 2/3 are from Scorpion Squadron and 1/3 are from Gunners Squadron.
So, we can write the following equation:
(3x + 2y)/(4x + 5y) = 2/3
Solving this equation, we get:
x/y = 5/4
Now, we can substitute this value in the equations for officers in each squadron:
Number of officers in Scorpion Squadron = 3x = 15k
Number of officers in Gunners Squadron = 2y = 10k
Therefore, the total number of officers in both squadrons is 25k.
Now, the probability of the chairperson being an officer can be calculated as:
Number of officers in Scorpion Squadron / Total number of officers in both squadrons
= 15k / 25k
= 3/5
= 0.714
Therefore, the probability of the chairperson being an officer is 25/42, which is option (a).
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