SOLUTION: The probabilities that Macy and Susan hit a target at each shot are 0.6 and 0.5 respectively. Assume that their result at each shot are independent. If each of them shoots at the t

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Question 1153745: The probabilities that Macy and Susan hit a target at each shot are 0.6 and 0.5 respectively. Assume that their result at each shot are independent. If each of them shoots at the target twice, find the probability that both Macy and Susan hit the target.
Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
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More accurate formulation to this problem is 

    The probabilities that Macy and Susan hit a target at each shot are 0.6 and 0.5 respectively. 
    Assume that their result at each shot are independent. If each of them shoots at the target twice, 
    find the probability that both Macy and Susan hit the target at least once.


Solution 

    P =  P(Macy hits only once of two shots)*P(Susan hits only once of two shots)
 
      +  P(Macy hits twice of two shots)*P(Susan hits only once of two shots) + 

      +  P(Macy hits only once of two shots)*P(Susan hits twice of two shots) + 

      +  P(Macy hits twice of two shots)*P(Susan hits twice of two shots) + 


      = C%5B2%5D%5E1%2A0.6%2A%281-0.6%29%2AC%5B2%5D%5E1%2A0.5%2A%281-0.5%29 + 0.6%5E2%2AC%5B2%5D%5E1%2A0.5%2A%281-0.5%29 + C%5B2%5D%5E1%2A0.6%2A%281-0.6%29%2A0.5%5E2 + 0.6%5E2%2A0.5%5E2 = 


      = 2%2A0.6%2A0.4%2A2%2A0.5%2A0.5 + 2%2A0.6%5E2%2A0.5%2A0.5 + 2%2A0.6%2A0.4%2A0.5%5E2 + 0.6%5E2%2A0.5%5E2 = 0.63.     ANSWER