Show all steps please S. A fair die is rolled over and over until a 3 is rolled.
ID: 3328322 • Letter: S
Question
Show all steps please
S. A fair die is rolled over and over until a 3 is rolled. (a) What is the probability that it will take exactly four rolls? (b) What is the expected value of this random variable? Interpret your answer. (c) What is the variance of this random variable? (d) What is the standard deviation of this random variable? An oil company conducts a geological research and concludes that an exploratory oil well has 0.15 chance of striking oil. 6. (a) What is the probability that the third strike comes in the sixth well drilled? (b) Determine the expected value and variance of this distribution. Interpret your answers. 7. A bag contains twenty marbles: six red and fourteen black. Five marbles are drawn without replacement. What is the probability that exactly two are red? If electricity power failures occur according to a Poisson distribution with an average of three failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week 8.Explanation / Answer
7)
there are total 20 balls
P(exactly two are red) , 5 balls are drawn so total sample space is 20C5
two red balls can be drawn from 6 red balls in 6C2 ways
remaining 3 balls can be drawn from the 14black balls in 14C3 ways
hence required probability is
(6C2 * 14C3)/ 20C5
6C2 = 15
C(n,r)=C(14,3)C(n,r)=C(14,3)
=14!(3!(143)!)=14!(3!(143)!)
= 364
and 20C5
C(n,r)=C(20,5)C(n,r)=C(20,5)
=20!(5!(205)!)=20!(5!(205)!)
= 15504
15*364/15504 = 0.3521
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