Questions: The table below gives probabilities for various combinations of events (A, B), and their complements. Probability of being in each cell of a two-way table A not A ------------------- B 0.2 0.4 not B 0.3 0.1 Find (P(textnot B)). Enter the exact answer. (P(textnot B)=)

The table below gives probabilities for various combinations of events (A, B), and their complements. Probability of being in each cell of a two-way table

A not A
-------------------
B 0.2 0.4
not B 0.3 0.1

Find (P(textnot B)). Enter the exact answer. (P(textnot B)=)

Transcript text: The table below gives probabilities for various combinations of events $A, B$, and their complements. Probability of being in each cell of a two-way table \begin{tabular}{|c|c|c|} \hline & A & not $A$ \\ \hline B & 0.2 & 0.4 \\ \hline not $B$ & 0.3 & 0.1 \\ \hline \end{tabular} Find $P(\operatorname{not} B)$. Enter the exact answer. $P($ not $B)=$

Solution

Solution Steps

Step 1: Identify the given probabilities

The table provides the probabilities for various combinations of events A, B, and their complements:

P(A and B) = 0.2
P(A and not B) = 0.4
P(not A and B) = 0.1
P(not A and not B) = 0.3

Step 2: Calculate the total probability of event B

To find P(B), sum the probabilities of all outcomes where B occurs: \[ P(B) = P(A \text{ and } B) + P(\text{not } A \text{ and } B) \] \[ P(B) = 0.2 + 0.1 = 0.3 \]

Step 3: Calculate the probability of not B

The probability of not B is the complement of the probability of B: \[ P(\text{not } B) = 1 - P(B) \] \[ P(\text{not } B) = 1 - 0.3 = 0.7 \]