Questions: Counting and Probability Probabilities of an event and its complement 1 2 3 4 5 6 7 8 9 10 ------------------------------------ X P(X)=1/5 not X P(not X)=4/5 (b) Subtract. 1-P(x)=4/5 (c) Select the answer that makes the sentence true. 1-P(X) is the same as (Choose one) P(not X) 1-P(not X) None of the above

Counting and Probability
Probabilities of an event and its complement

1 2 3 4 5 6 7 8 9 10
------------------------------------
X P(X)=1/5
not X P(not X)=4/5

(b) Subtract.
1-P(x)=4/5

(c) Select the answer that makes the sentence true.
1-P(X) is the same as (Choose one)
P(not X)
1-P(not X)
None of the above

Transcript text: Counting and Probability Probabilities of an event and its complement \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{1}{|c|}{} & \multicolumn{7}{|c|}{ Putcomes } \\ \hline & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & \\ \hline$X$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $P(X)=\frac{1}{5}$ \\ \hline not $X$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $\square$ & $P(\operatorname{not} X)=\frac{4}{5}$ \\ \hline \end{tabular} (b) Subtract. $1-P(x)=\frac{4}{5}$ (c) Select the answer that makes the sentence true. $1-P(X)$ is the same as $\square$ (Choose one) $P(\operatorname{not} X)$ $1-P(\operatorname{not} X)$ None of the above

Solution

Solution Steps

Solution Approach

Part (b): To find $1 - P(X)$, we subtract the probability of event $X$ from 1. Given $P(X) = \frac{1}{5}$, we calculate $1 - \frac{1}{5}$.
Part (c): We need to determine which option is equivalent to $1 - P(X)$. Since $1 - P(X)$ is the probability of the complement of $X$, it should be equal to $P(\text{not } X)$.

Step 1: Calculate $1 - P(X)$

Given that $P(X) = \frac{1}{5}$, we calculate the complement probability as follows: \[ 1 - P(X) = 1 - \frac{1}{5} = \frac{5}{5} - \frac{1}{5} = \frac{4}{5} \]

Step 2: Determine the Equivalent Expression

We need to determine which option is equivalent to $1 - P(X)$. Since $1 - P(X) = \frac{4}{5}$ and $P(\text{not } X) = \frac{4}{5}$, it follows that: \[ 1 - P(X) = P(\text{not } X) \]