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A security system allows each user up to 4 password attempts per day. Each attempt is independent and has probability 0.3 of succeeding. Let
be the number of successful attempts.
Complete the following probability distribution table for X, to three decimal places.
Find the expectation E(X) and the variance Var(X).
Determine P(X≥2).
On a given day, 20 independent users each take up to 4 attempts. Let
State the distribution and parameters of Y.
Find E(Y).
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At an airport car-rental depot the staff record two events for every car that is returned:
C : Car requires exterior cleaning.
L : Fuel level is low (below ½ tank).
From long term data, they estimate that P(C)=0.35,P(L)=0.25, and P(C∩L)=0.12.
Find P(C′∩L′)
Find the probability that exactly one of the two events occurs.
Determine P(C∣L).
State, and justify, whether events C and L appear to be independent.
On a particular day 12 cars are returned.
Assume that whether any individual car requires exterior cleaning is independent of the others.
State the distribution of the random variable X= number of cars that require cleaning that day.
Find
P(X=6).
P(X≥4).
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