Question

use the contingency table to the right to determine the probability of events.
a. what is the probability of event a?
b. what is the probability of event a?
c. what is the probability of event a and b?
d. what is the probability of event a or b?

a. the probability of event a is \boxed{}.
(type an integer or decimal rounded to three decimal places as needed.)

contingency table:
b b
a 50 60
a 30 50

Explanation:

Step1: Find total number of outcomes

First, we calculate the total number of elements in the contingency table. We sum up all the values: \(50 + 60 + 30 + 50 = 190\).

Step2: Find number of outcomes for event A

Event A includes the values 50 (for A and B) and 60 (for A and \(B'\)). So the number of outcomes for event A is \(50 + 60 = 110\).

Step3: Calculate probability of event A

The probability of an event is the number of favorable outcomes divided by the total number of outcomes. So the probability of event A, \(P(A)\), is \(\frac{110}{190}\). Simplifying this, we get \(\frac{11}{19} \approx 0.5789\), rounded to three decimal places is \(0.579\).

Answer:

\(0.579\)