Question

Penny drives the same route to work every day. There are 6 traffic lights along the route. For each light there is a 75% chance that the light is red when Penny arrives and a 25% that it is green. The lights operate independently of one another. Let X equal the number of these lights which are red when Penny arrives. a) What is the probability that $X = 6$? b) What is the probability that $X = 4$? c) What is the probability that fewer than 4 traffic lights are red when Penny arrives? d) What is the expected value of $X$? e) What is the expected value of $X^{2.4}$?

          Penny drives the same route to work every day. There are 6 traffic lights along the route. For each light there is a 75% chance that the light is red when Penny arrives and a 25% that it is green. The lights operate independently of one another. Let X equal the number of these lights which are red when Penny arrives.
a) What is the probability that $X = 6$? 

b) What is the probability that $X = 4$? 

c) What is the probability that fewer than 4 traffic lights are red when Penny arrives?

d) What is the expected value of $X$?

e) What is the expected value of $X^{2.4}$?

Penny drives the same route to work every day. There are 6 traffic lights along the route. For each light there is a 75% chance that the light is red when Penny arrives and a 25% that it is green. The lights operate independently of one another. Let X equal the number of these lights which are red when Penny arrives.
a) What is the probability that X = 6?

b) What is the probability that X = 4?

c) What is the probability that fewer than 4 traffic lights are red when Penny arrives?

d) What is the expected value of X?

e) What is the expected value of X^2.4?

Added by Andrea P.

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