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If the probability that it may rain tomorrow is 2/5, what is the probability that it may not rain?
When a coin is tossed 5 times, how many possible outcomes are expected to be listed in the sample space?
How many different permutations can be made from the letters in the word “CHICHARITO”?
A coin is flipped and a die is rolled. Find the probability of getting a tail on the coin and a 3 on the die.
Determine the unique solution of the following differential equations by using Laplace transforms:
y''(t) + 2y'(t) -3y(t) = e-3t if y'(0) = 0 and y(0) = 0
Determine the unique solution of the following differential equations by using Laplace transforms:
y''(t)-6y'(t)+9y(t) = t2e3t if y'(0) = 6 and y(0) = 2
3. The geometrical representation of a vector v =
a
b
is an arrow starting at the origin and ending at the point (a, b).
Multiplication of a vector v with the matrix A =
cos θ − sin θ
sin θ cos θ
yields a vector p =Av
which is a counter clockwise rotation of v by an angle of θ.
a) Find the vector p that is obtained if v =
3
−4
is rotated counter clockwise by 40◦
.
b) Find the vector q that is obtained if v =
2
3
is rotated clockwise by 40◦
.
Determine L-1{es(s2-1/(s2+1)2)}
Determine whether W = {(x, y,z) | x + y + z + 1 = 0, x, y,z ∈ R} a subspace of R³ or
not?
7. In the classic legal case of Whitus v. Georgia, a jury pool of 90 people was supposed to be randomly selected from a population in which 27% were minorities. Among the 90 people selected, 7 were minorities.
(a) Can we use a normal approximation to find the approximate probability of getting 7 or fewer minorities if the jury pool was randomly selected? If so, find it.
(b) What does the result suggest about the jury selection process?
#340153 on Dec 2023