Question

five balls numbered from 1 to 5 are placed into a bag.
some are grey and some are white.
the balls numbered 2, 4, and 5 are grey.
the balls numbered 1 and 3 are white.
a ball is selected at random.
let x be the event that the selected ball is white, and let ( p(x) ) be the probability of x.
let not x be the event that the selected ball is not white, and let ( p(\text{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(x)=square )

Explanation:

Step1: Determine the number of favorable outcomes and total outcomes for event \(X\)

Total number of balls \(n = 5\).
Number of white balls (favorable for \(X\)) \(m=2\) (balls numbered \(1\) and \(3\)).
Probability formula \(P(X)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
So, \(P(X)=\frac{2}{5}\).

Step2: Determine the number of favorable outcomes and total outcomes for event \(\text{not }X\)

Number of non - white balls (favorable for \(\text{not }X\)) \(k = 3\) (balls numbered \(2\), \(4\), \(5\)).
Using the probability formula \(P(\text{not }X)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
So, \(P(\text{not }X)=\frac{3}{5}\).

Step3: Calculate \(1 - P(X)\)

Substitute \(P(X)=\frac{2}{5}\) into \(1 - P(X)\).
\(1-\frac{2}{5}=\frac{5 - 2}{5}=\frac{3}{5}\).

Answer:

• For event \(X\): Check the boxes for \(1\) and \(3\), \(P(X)=\frac{2}{5}\)
• For event \(\text{not }X\): Check the boxes for \(2\), \(4\), and \(5\), \(P(\text{not }X)=\frac{3}{5}\)
• For \(1 - P(X)\): \(1 - P(X)=\frac{3}{5}\)