Coin A is flipped 4 times and coin B is flipped 5 times. What is the probability that the number of heads obtained from flipping the two coins is the same?


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Answer:

 

63
256
 

Step by Step Explanation:
  1. The situation of having the same number of heads obtained will occur when 0, 1, 2, 3, and 4 heads appear in both the coins.
    So, let's find the individual probability for each scenario and then we will add the probabilities to find the probability of combined scenarios.
  2. The probability of getting 0 heads in both coins will be:
    ( 
    1
    2
     )4 × 4C0 × ( 
    1
    2
     )5 × 5C0
    =  
    1
    512
     
  3. The probability of getting 1 heads in both coins will be:
    ( 
    1
    2
     )4 × 4C1 × ( 
    1
    2
     )5 × 5C1
    =  
    20
    512
     
  4. The probability of getting 2 heads in both coins will be:
    ( 
    1
    2
     )4 × 4C2 × ( 
    1
    2
     )5 × 5C2
    =  
    60
    512
     
  5. The probability of getting 3 heads in both coins will be:
    ( 
    1
    2
     )4 × 4C3 × ( 
    1
    2
     )5 × 5C3
    =  
    40
    512
     
  6. The probability of getting 4 heads in both coins will be:
    ( 
    1
    2
     )4 × 4C3 × ( 
    1
    2
     )5 × 5C3
    = 
    5
    512
     
  7. The probability of getting same number heads in both coins will be a sum of all above individual probabilities:  
    1
    512
      +  
    20
    512
      +  
    60
    512
      +  
    40
    512
      +  
    5
    512
     
    =  
    126
    512
     
    =  
    63
    256
     

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