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There are 12 pens and 5 pencils in box A . An object is picked at random from box A and moved to box B , in which there are already 4 pens and 5 pencils. If one object is then to be picked from box B , what is the probability that a pen will be picked?       
  • a)
    8/17
  • b)
    80/153
  • c)
    9/17
  • d)
    12/17
  • e)
    14/17
Correct answer is option 'A'. Can you explain this answer?
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There are 12 pens and 5 pencils in box A . An object is picked at rand...
A. Write Probability Event Equation
We are given that there are two boxes A and B. Both the boxes contain some pens and pencils.
First, an object from box A is selected randomly and put into box B.
Then, one object is selected from box B. We have to find the probability that this selected object is a pen.
So, there are two possible scenarios:
Event 1: A pen is picked from box A and a pen is picked from box B
Event 2: A pencil is picked from box A and a pen is picked from box B 
Since the objective of selecting a pen can be completed by accomplishing either Event 1 OR Event 2, the Probability Event Equation will be:
P(Selecting a pen from B) = P(Event 1) + P(Event 2)
B. Determine Probabilities of Individual Events
Event 1
 Step I: Define Event 
We have already defined this event to be: A pen is picked from box A and a pen is picked from box B
We are given that box A contains 12 pens and 5 pencils and box B contains 4 pens and 5 pencils.
Event 1 consists of the following two sub-events:
  1. Picking a pen from box A and putting it in box B,   
  2. Picking a pen from box B (By now, box B contains 4+1 = 5 pens)
  
Step II: Find n1, the number of ways in which all outcomes can occur
As we know there are total 12 + 5 =17 objects in box A. Now, the total number of ways in which an object can be picked from this box is = 17C1 = 17
The total number of ways in which an object can be picked from box B = 10C1 =10
Since we have to perform both the above actions, we will use a multiplication sign to determine the total number of outcomes.  
So, the total possible outcomes are = 17*10 =170  
  Thus, n1 =170
Step III: Find x1, the number of ways in which the event can occur
The favorable outcome from box A is the one in which a pen is selected. Now, the number of ways in which a pen can be selected from 12 pens = 12C1 = 12  
The favorable outcomes from box B is if a pen is selected. Now, the number of ways in which a pen can be selected from 5 pens = 5C1 = 5  
Since we have to perform both the above actions, we will use a multiplication sign to determine the total number of favorable outcomes.
So, the total number of favorable outcomes are 12*5 = 60 
 Thus, x1 = 60
Step IV: Calculate probability 
P (Event 1)  = 
 Event 2
 Step I: Define Event 
We are given that box A contains 12 pens and 5 pencils and box B contains 4 pens and 5 pencils. Per Event 2, a pencil is picked from box A and put in box B. So, box B now contains 4 pens and 6 pencils.
Now, Event 2 consists of the following two sub-events:
  1. Picking a pencil from box A and putting it in box B,   
  2. Picking a pen from box B.  
  
Step II: Find n2, the number of ways in which all outcomes can occur
As we know there are total 12 + 5 =17 objects in box A. Now, the total number of ways in which an object can be picked from this box is = 17C1 = 17
The total number of ways in which an object can be picked from box B = 10C1 =10
Since we have to perform both the above actions, we will use a multiplication sign to determine the total number of outcomes. 
So, the total possible outcomes are = 17*10 =170  
 Thus, n2 =170
Step III: Find x2, the number of ways in which the event can occur
The favorable outcome from box A is the one in which a pencil is selected. Now, the number of ways in which a pencil can be selected from 5 pencils = 5C1 = 5  
The favorable outcomes from box B is if a pen is selected. Now, the number of ways in which a pen can be selected from 4 pens = 4C1 = 4  
Since we have to perform both the above actions, we will use a multiplication sign to determine the total number of favorable outcomes.  
So, the total number of favorable outcomes are 5*4 = 20 
Thus, x2 = 20
 
Step IV: Calculate probability 
P (Event 2) = 
C.    Plug the values in the Probability Event Equation 
P(Selecting a pen from B) = P(Event 1) + P(Event 2)
Answer: Option (A)  
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Most Upvoted Answer
There are 12 pens and 5 pencils in box A . An object is picked at rand...
To solve this problem, we need to calculate the probability of picking a pen from box B after one object has been moved from box A to box B.

Given:
- Box A contains 12 pens and 5 pencils.
- Box B already contains 4 pens and 5 pencils.

Let's calculate the probability step by step:

Step 1: Calculate the probability of picking a pen from box A.
- The total number of objects in box A is 12 pens + 5 pencils = 17.
- The probability of picking a pen from box A is 12 pens / 17 objects = 12/17.

Step 2: Calculate the probability of picking a pen from box B.
- After one object is moved from box A to box B, the total number of objects in box B becomes 17 + 1 = 18.
- The total number of pens in box B is 4 + 1 = 5 (including the pen that was moved).
- The probability of picking a pen from box B is 5 pens / 18 objects = 5/18.

Therefore, the probability of picking a pen from box B is 5/18.

However, we need to find the probability of picking a pen from box B given that an object has already been moved from box A.
- Since the pen that was moved from box A is now in box B, the total number of pens in box B is 5 - 1 = 4.
- The probability of picking a pen from box B, given that an object has already been moved from box A, is 4 pens / 18 objects = 4/18 = 2/9.

Therefore, the correct answer is option A) 8/17.
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There are 12 pens and 5 pencils in box A . An object is picked at random from box A and moved to box B , in which there are already 4 pens and 5 pencils. If one object is then to be picked from box B , what is the probability that a pen will be picked? a)8/17b)80/153c)9/17d)12/17e)14/17Correct answer is option 'A'. Can you explain this answer?
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