The probability of a snowstorm...

Question

The probability of a snowstorm on Thanksgiving is 0.22, and the probability of a snowstorm on Christmas is 0.65. Assuming that these two events are independent.

 

What is the probability of snowstorms on both?

 

What is the probability of a snowstorm on either thanksgiving or christmas?

 

What is the probability of a snowstorm on thanksgiving but not on christmas?

Answer 1

Hello,

Once you know that the 2 events are independent, then you know that  P(A∩B) = P(A) x P(B)

P(A∩B) means the probability of both A and B

 

so if A= snowstorm on Thanksgiving

and B = snowstorm on Christmas

 

Then Probability of snowstorm on both means P(A∩B) = 0.22 x 0.65 = 0.143

 

Probability of snowstorm in either means Probability of A Union B ...  P(A∪B) = P(A) + P(B) -P(A∩B) 

 so P(A∪B) = 0.22 + 0.65 - 0.143 = 0.727

 

 

 

probability of a snowstorm on thanksgiving but not on Christmas is simply P(A) - P(A∩B)  = 0.22- 0.143 = 0.077

 

I hope this made sense to you

 

Hazim Fanik

 

Answer 2

Hi Shelby,

 

The key concept here is that the two events are INDEPENDENT.  This means you can simply multiply the probabilities of the outcomes you're interested in.  For example,  if two events, A and B, are independent and P(A) = 1/4 and P(B) = 2/5, then P(A and B) = (1/4)*(2/5) = 1/10.  And the probability of A only is P(A)*[1-P(B)] because 1-P(B) is the probability that B doesn't happen.

 

NOTE: P(A) is notation for "the probability of A".  

 

Does this help?