\\Q:Would like to understand these examples of Statistics with the steps of the

Question

Q:Would like to understand these examples of Statistics with the steps of the solution to better understand, thanks.

a) An oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. What is the probability that the first strike comes on the third well drilled?

b) There are six bulbs in a house out which 3 are defective. If 2 bulbs are picked randomly, find the probability that at least one is defective.

c) Given : the probability that a student passes the written exam for a driver's license is 0.75. Question: What is the probability that a student will fail on the first two attempts and pass on the third? State which probability distribution --- Binomial, Geometric, or Poisson --- applies to the question. DO NOT ATTEMPT TO COMPUTE THE ANSWER!!!

Explanation / Answer

a) P(Striking oil) = 0.20

So,

P(Not striking) = 1 - 0.20 = 0.80

P(First strike comes on third well)

= P(No strike on first well)*P(No strike on second well)*P(Strike on third well)

= 0.8*0.8*0.2

= 0.128

b) P(Defective) = P(Not defective) = 3/6 = 0.5

So,

P(At least one defective)

= 1 - P(No defective)

= 1 - (3/6)*(2/5)

= 1 - 1/5

= 4/5

= 0.80

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