Math

QuestionIf P(B)=0.2P(B)=0.2, find P(BC)P\left(B^{C}\right). P(BC)=P\left(B^{C}\right)=

Studdy Solution

STEP 1

What is this asking? If the probability of event B happening is 0.2, what's the probability of event B *not* happening? Watch out! Don't forget that probabilities always add up to **one**!

STEP 2

1. Define the relationship between P(B)P(B) and P(BC)P(B^C).
2. Calculate P(BC)P(B^C).

STEP 3

Alright, so we know that something *either* happens or it doesn't!
That means the probability of event B happening, plus the probability of B *not* happening (written as P(BC)P(B^C)), has gotta equal **one**!
It's a sure thing!

STEP 4

Mathematically, we can write this super important relationship as: P(B)+P(BC)=1 P(B) + P(B^C) = 1 This is like our golden rule here!

STEP 5

We're given that P(B)=0.2P(B) = \textbf{0.2}, and we want to find P(BC)P(B^C).
Let's plug our known value into our golden rule equation: 0.2+P(BC)=1 \textbf{0.2} + P(B^C) = 1

STEP 6

Now, to get P(BC)P(B^C) all by itself, we need to subtract **0.2** from *both* sides of the equation.
Remember, what we do to one side, we *must* do to the other to keep things balanced! P(BC)=10.2 P(B^C) = 1 - \textbf{0.2}

STEP 7

And that gives us our final answer: P(BC)=0.8 P(B^C) = \textbf{0.8} Boom!

STEP 8

P(BC)=0.8 P(B^C) = 0.8

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