Three little pigs were at home when the big, bad wolf tried to blow their house

Question

Three little pigs were at home when the big, bad wolf tried to blow their house in. There is a 25% chance that the wolf will successfully blow down the little pigs' house on any given day. (Try not to overthink this problem!) a) Use the correct probability notation for parts b, c, and d. b) What are the chances (probability) that the big, bad wolf will not blow down the house? Define the event B =____ c) Every day for 4 days the big, bad wolf tried to blow down the pigs' house. What are the chances the big, bad wolf is unsuccessful on all 4 days? What assumption did you have to make to complete this problem? d) What are the chances that the big bad wolf is successful on at least 1 of the 4 days he tries? (Let's assume that the pigs can rebuild their house instantly if it gets blown in. Hey, a wolf is blowing down a house, so I'm sure many other magical things can also happen too.)

Explanation / Answer

B) Let B be the event that the wolf will blow away the pig's house

P(B) = 0.25

So, the probability that the wolf will not blow down the house = P(B')

= 1 - P(B)

= 1 - 0.25

= 0.75

C) when we consider 4 days, its a binomial distribution, B(4, 0.25)

P(wolf was successfull on all 4 bays) = P(4) = 4C4 x 0.254 x 0.750

= 0.0039

D) P(successfull on at least 1 of the 4 days) = 1 - P(not successful on all 4 days)

= 1 - P(0)

= 1 - 0.754

= 0.3164

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