Question

If p(a) = 0.33, find p(ac). question 8 options: 0.33 0.335 0.67 0.165

Answer 1

p(ac) = 1 - p(a) = 1 - 0.33 = 0.67 the probability of the complement of event A in this scenario is 0.67, signifying the likelihood of outcomes not falling into event A.

Step-by-step explanation:

To find the probability of the complement of event A, denoted as p(ac), we utilize the fact that the sum of probabilities of an event and its complement equals 1. Given that p(a) = 0.33, we can determine p(ac) by subtracting the probability of event A from 1.

In probability theory, the complement of an event refers to all outcomes not included in that event. Thus, if the probability of event A occurring is 0.33, the probability of its complement, not A (denoted as ac), occurring can be calculated as 1 - 0.33 = 0.67. This calculation stems from the fundamental concept that the sum of the probabilities of an event and its complement is always equal to 1.

Therefore, the probability of the complement of event A in this scenario is 0.67, signifying the likelihood of outcomes not falling into event A.

Answer 2

The correct option is C) 0.67.

To find P(AC), which is the probability of the complement of event A, we use the basic probability rule :

P(A) + P(AC) = 1

According to this rule, the total probability of an event and its complement must equal to 1, because the two events cover all possible outcomes.

Given that P(A) = 0.33, we can substitute this value into our equation :

0.33 + P(AC) = 1

Now, we want to solve P(AC). To do this, we'll subtract the probability of event A from 1 :

P(AC) = 1 - 0.33
P(AC) = 0.67

P(AC), the probability of the complement of event A, is 0.67.