If a, b, and c are mutually exclusive events with p(a) = 0.2, p(b) = 0.3, and p(c) = 0.4, determine the following probabilities: a. p(a ∪ b ∪ c) b. p(a ∩ b ∩ c) c. p(a ∩ b) d. p[(a ∪ b) ∩ c] e. p(a′ ∩ b′ ∩ c′)

a. The events are mutually exclusive, so

b. For the same reason,

Another way to see this is to use the result from part (a), and the inclusion/exclusion principle:

and the right side reduces to 0.

c. Same as (b),

d. Same as (b),

We can also use the distributivity rule for unions and intersections to write

e. If the is the complement of , then by DeMorgan's law,

no, the equation would be invalid since they are both not equal.

step-by-step explanation:

here you got

4y-6+4y 2-9

first, you would simplify the equation on the form.

4y-6+4y 2-9

then, move all the terms that contains a y to the left and all the other terms to the right.

+4y-4y+-9-6

finally, you will simplify the left and the right side of the equation.

y=-3