Question

we have a deck of 10 cards numbered from 1 to 10. some are grey and some are white. the cards numbered 1, 7, and 9 are grey. the cards numbered 2, 3, 4, 5, 6, 8, and 10 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 outcomes probability 1 2 3 4 5 6 7 8 9 10 x □ □ □ □ □ □ □ □ □ □ p(x)=□ not x □ □ □ □ □ □ □ □ □ □ p(not x)=□

Explanation:

Step1: Calculate number of favorable outcomes for X

Grey - numbered cards are 1, 7, 9. So number of favorable outcomes for X is 3.

Step2: Calculate P(X)

Total number of cards is 10. Probability formula is $P(X)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P(X)=\frac{3}{10}$.

Step3: Calculate number of favorable outcomes for not X

Cards that are not grey are 2, 3, 4, 5, 6, 8, 10. So number of favorable outcomes for not X is 7.

Step4: Calculate P(not X)

Using the probability formula, $P(\text{not }X)=\frac{7}{10}$.

Answer:

For event X:

• Outcomes: Check 1, 7, 9
• $P(X)=\frac{3}{10}$

For event not X:

• Outcomes: Check 2, 3, 4, 5, 6, 8, 10
• $P(\text{not }X)=\frac{7}{10}$