(A^C)^C

(A^C)^C
we read this as The complement of the Complement of Set A
The complement of set A is anything NOT in A.
But the complement of the complement is anything NOT NOT IN A.
Which is just [B]A
[MEDIA=youtube]-eo-Bq6qZVM[/MEDIA][/B]

A bag contains 10 red balls, 10 green balls and 6 white balls. Two balls are drawn at random from th

A bag contains 10 red balls, 10 green balls and 6 white balls. Two balls are drawn at random from the bag without replacement. What is the probability that they are of different colours?
[LIST]
[*]The key phrase here is [I]without replacement[/I].
[*]First, it's easier to find the probability of both colors matching, and then subtracting that from 1.
[/LIST]
We want 1 - (P(Red-Red) + P(Green-Green) + P(White-White)). So we have the following:
[U]Find the probability of both colors matching[/U]
P(Red-Red) = 10/26 * 9/25 = 0.138462
P(Green-Green) = 10/26 * 9/25 = 0.138462
P(White-White) = 6/26 * 5/25 = 0.046154
P(Red-Red) + P(Green-Green) + P(White-White) = 0.13846 + 0.13846 + 0.046154 = 0.3231
Now, we want to take the complement of this probability which is no colors matching, so we have:
P(Both Different Colors) = 1 - P(Same Colors)
P(Both Different Colors) = 1 - 0.3231
P(Both Different Colors) = [B]0.6769[/B]

An angle is 30 degrees less than 5 times it's complement. Find the angle.

An angle is 30 degrees less than 5 times it's complement. Find the angle.
Let the angle be a. The complement of a is 90 - a. We're given the following equation:
a = 5(90 - a) - 30 <-- Less means we subtract
Multiplying though, we get:
a = 450 - 5a - 30
a = 420 - 5a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%3D420-5a&pl=Solve']Typing this equation into our search engine[/URL], we get:
a =[B] 70[/B]

Complementary and Supplementary Angles

Free Complementary and Supplementary Angles Calculator - This calculator determines the complementary and supplementary angle of a given angle that you enter OR it checks to see if two angles that you enter are complementary or supplementary.

If the probability of rain is 15%, what is the probability that it won't rain?

If the probability of rain is 15%, what is the probability that it won't rain?
If we assign the probability of raining as event A, then A' (A complement) is the probability it won't rain. Since it either rains or doesn't rain are the only two events.
There exists an axiom in statistics that states:
P(A) + P(A') = 1
Rearranging this, we get:
P(A') = 1 - P(A)
If we assign the probability of raining as event A which is 0.15, we get:
P(A') = 1 - 0.15
P(A') = [B]0.85[/B]

In rolling a die, the event E is getting a number greater than or equal to 3. What is the complement

In rolling a die, the event E is getting a number greater than or equal to 3. What is the complement of the event?
The complement E' is everything but the event. So we have:
E = P(n >= 3)
E' = [B]P(n < 3)[/B]

Sets

Free Sets Calculator - This lesson walks you through what a set is, how to write a set, elements of a set, types of sets, cardinality of a set, complement of a set.

True or False (a) The normal distribution curve is always symmetric to its mean. (b) If the variance

True or False
(a) The normal distribution curve is always symmetric to its mean.
(b) If the variance from a data set is zero, then all the observations in this data set are identical.
(c) P(A AND A^{c})=1, where A^{c} is the complement of A.
(d) In a hypothesis testing, if the p-value is less than the significance level ?, we do not have sufficient evidence to reject the null hypothesis.
(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.
[B](a) True, it's a bell curve symmetric about the mean
(b) True, variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical
(c) True. P(A) is the probability of an event and P(Ac) is the complement of the event, or any event that is not A. So either A happens or it does not. It covers all possible events in a sample space.
(d) False, we have sufficient evidence to reject H0.
(e) False. Volume can be a decimal or fractional. There are multiple values between 127 and 128. So it's continuous.[/B]

Venn Diagram

Free Venn Diagram Calculator - This lesson walks you through what a Venn diagram is, the Venn diagram for A union B, A intersection B, and A Complement.