Questions: We have a deck of 8 cards numbered from 1 to 8.
Some are grey and some are white.
The cards numbered 3, 4, 5, 6, 7, and 8 are grey.
The cards numbered 1 and 2 are white.
A card is drawn at random.
Let X be the event that the drawn card is grey, and let P(X) be the probability of X.
Let not X be the event that the drawn card is not grey, and let P(not X) be the probability of not X.
(a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.
Event 1 2 3 4 5 6 7 8 Probability
----- - - - - - - - - ------------
X O O O O O O P(X)=
not X O O P(not X)=
(b) Subtract.
1-P(not X)=
(c) Select the answer that makes the sentence true.
1-P(not X) is the same as (Choose one)
Transcript text: We have a deck of 8 cards numbered from 1 to 8.
Some are grey and some are white.
The cards numbered 3, 4, 5, 6, 7, and 8 are grey.
The cards numbered 1 and 2 are white.
A card is drawn at random.
Let $X$ be the event that the drawn card is grey, and $\operatorname{let} P(X)$ be the probability of $X$.
Let not $X$ be the event that the drawn card is not grey, and let $P($ not $X)$ be the probability of not $X$.
(a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline & \multicolumn{8}{|c|}{Outcomes} & \\
\hline Event & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & Probability \\
\hline $X$ & & & O & O & O & O & O & O & $P(X)=\square$ \\
\hline not $X$ & O & O & & & & & & & $P(\operatorname{not} X)=\square$ \\
\hline
\end{tabular}
(b) Subtract.
\[
1-P(\operatorname{not} X)=
\]
$\square$
(c) Select the answer that makes the sentence true.
$1-P(\operatorname{not} X)$ is the same as (Choose one)
$\square$
Solution
Solution Steps
Step 1: Identify the Total Number of Items (N)
The total number of items in the set is 8.
Step 2: Identify the Number of Items with the Specified Attribute (M)
The number of items with the attribute 'grey' is 6.
Step 3: Calculate the Probability (P)
The probability of drawing an item with the attribute 'grey' is calculated as follows:
\[P = \frac{M}{N} = \frac{6}{8} = 0.75\]
Step 4: Calculate the Probability of Not Drawing an Item with the Specified Attribute (P(not X))
The probability of not drawing an item with the attribute 'grey' is calculated as follows:
\[P(\text{not } X) = 1 - P(X) = 1 - 0.75 = 0.25\]
Final Answer:
The probability of drawing an item with the attribute 'grey' is 0.75,
while the probability of not drawing an item with the attribute 'grey' is 0.25.