Question 1196465
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You posted way too many questions. 
The official rule is <font size=4><u>one</u></font> question per post. 
Sometimes, if the questions are fairly short, then a few can be squeezed in together (which is useful if they are related questions). Though in my opinion it's better to stick to the official rule. 


I'll do question 1 to get you started.


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Question:
1.An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 57% probability of winning the first contract. If they win the first contract, the probability of winning the second is 67%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 44%.
What is the probability that they lose both contracts?




Solution:
There's a 57% chance of getting the first contract. 
That means there's a 100% - 57% = 43% chance of not winning the first contract.
This converts to the decimal form 0.43


It states that if the first contract is lost, then the probability of winning the second contract is 44%
So there's a 100% - 44% = 56% chance of losing the second contract if the first contract was lost.
This converts to the decimal form 0.56


Multiply those decimal values to get 0.43*0.56 = 0.2408 = <font color=red>24.08%</font> which is the probability of losing both contracts in a row. 


Edit: @ikleyn makes a good point about independent vs dependent events. However, I'm using the idea that P(A and B) = P(A)*P(B given A). So multiplication is still valid here. 
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