Calculating Probability of Union of Two Events

Find the probability of the indicated event if ​P(E)equals0.30 and ​P(F)equals0.55. Find​ P(E or​ F) if​ P(E and ​F)equals0.05. Question content area bottom Part 1 ​P(E or ​F)equals    enter your response here ​(Simplify your​ answer.)

To find ( P(E \text{ or } F) ), we can use the formula for the probability of the union of two events:

[ P(E \text{ or } F) = P(E) + P(F) - P(E \text{ and } F) ]

Given:

• ( P(E) = 0.30 )
• ( P(F) = 0.55 )
• ( P(E \text{ and } F) = 0.05 )

Now, substituting the values into the formula:

[ P(E \text{ or } F) = 0.30 + 0.55 - 0.05 ]

Calculating this step-by-step:

1. ( 0.30 + 0.55 = 0.85 )
2. ( 0.85 - 0.05 = 0.80 )

Thus,

[ P(E \text{ or } F) = 0.80 ]

So, the final answer is:

[ \boxed{0.80}