Two symptoms are associated with a certain disease.
there is a 95% probability that at least one of the symptoms occurs;
in addition, the first symptom occurs with 50% probability, the second symptom occurs with 45% probability.
based on these probability results, answer the following two questions
1) are the two events "first symptom occurs" and "second symptom occurs" mutually exclusive (i. e. disjoint)?
2) are the two events "first symptom occurs" and "second symptom occurs" independent?
for each question, clearly state yes or no and provide a brief written explanation that includes the appropriate numerical support.

Mutually exclusive, dependent events

Step-by-step explanation:

Two events A and B are mutually exclusive if

Two events A and B are independent if

Remark: All mutually exclusive events are dependent.

Now,

A = the first symptom occurs

B = the second symptom occurs

Use the rule

Thus, the events A and B are mutually exclusive (disjoint) and dependent (accordint to the remark)

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .