Question

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.
(b) subtract.
1 - p(not x) =
(c) select the answer that makes the sentence true.
1 - p(not x) is the same as select.

Explanation:

Step1: Identify outcomes for event X

Event X is the card being grey. From the table, the outcomes for X are 1,7,9.

Step2: Calculate \(P(X)\)

There are 10 total cards. The number of favorable outcomes (grey cards) is 3. So \(P(X)=\frac{3}{10}\)

Step3: Calculate \(P(\text{not }X)\)

Use the formula \(P(\text{not }X)=1 - P(X)\). Substitute \(P(X)=\frac{3}{10}\), so \(P(\text{not }X)=1-\frac{3}{10}=\frac{7}{10}\)

Answer:

(a) Outcomes for \(X\): 1,7,9; (b) \(1 - P(\text{not }X)=\frac{3}{10}\) (c) \(1 - P(\text{not }X)\) is the same as \(P(X)\)