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March 30th, 2016, 10:23 AM  #1 
Newbie Joined: Feb 2016 From: Colorado Posts: 28 Thanks: 0  Understanding how to figure these out
There are 10 houses on the street where you live. On a snowy day, the probability that someone will shovel the driveway by hand is 65%. What is the probability that less than 4 driveways will be shoveled by hand? There are 8 houses on the street where you live. On a snowy day, the probability that someone will shovel the driveway by hand is 60%. What is the probability that more than 4 driveways will be shoveled by hand? The probability that a person owns an iPAD is 0.32. The probability that, given the person owns an iPad, he/she attends Fairview is 0.12. What is the probability that a person owns an iPAD and attends Fairview? 
March 30th, 2016, 10:47 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
Assuming that each shovelling is independent, for 1) and 2), you can apply the formula for the pmf of a binomial distribution. For the first one, the probability is $\displaystyle 0.35^{10} + \displaystyle{10 \choose 1}0.65^1 \times 0.35^9 + \displaystyle{10 \choose 2}0.65^2 \times 0.35^8 + \displaystyle{10 \choose 3}0.65^3 \times 0.35^7$. I think you can do the other one now. For the third question, let I be the event that the person owns an iPad and F be the event that he attends Fairview. P(I) = 0.32, P(FI) = 0.12. P(I ∩ F) = P(I)P(FI) = 0.32 * 0.12 = 0.0384. 
March 30th, 2016, 12:46 PM  #3  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896  Quote:
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March 30th, 2016, 07:06 PM  #4 
Newbie Joined: Feb 2016 From: Colorado Posts: 28 Thanks: 0  Confused
I am confused with the probability of less than four driveways being shoveled.

March 31st, 2016, 12:24 PM  #5 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 634 Thanks: 85  

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