Question

Consider the following probabilities: p(ac) = 0.30, p(b) = 0.60, and p(a ∩ bc) = 0.24. What is the probability of event a?

1) 0.06
2) 0.30
3) 0.54
4) 0.84

Answer 1

The probability of event 'a' is found by adding P(ac) and P(a ∩ bc), which gives P(a) = 0.54. This is calculated using the addition rule of probability, leading to the correct answer, option 3) 0.54.

Step-by-step explanation:

To find the probability of event a, we'll use the given probabilities and some properties of probability. We know P(ac) = 0.30 and P(a ∩ bc) = 0.24, where 'c' represents the complement of event 'b'. According to the addition rule of probability, for any two events 'a' and 'b': P(a) = P(ac) + P(a ∩ bc)

Using this rule, we can calculate the probability of event 'a' as follows:

• 
  
• 
  
• 
  

Thus, the probability of event 'a' is 0.54. Therefore, the correct choice from the given options is 3) 0.54.