Questions: Consider the following Venn diagram, where P(E1) = P(E2) = P(E3) = 1/5, P(E4) = P(E5) = 1/20, P(E6) = 1/10, and P(E7) = 1/5. Complete a through h. Click the icon to view the Venn diagram. a. Find P(A). P(A) = 1 (Type an integer or a simplified fraction.)

Solution Steps

The problem provides the following probabilities:

• $P(E_1) = P(E_2) = P(E_3) = P(E_7) = \frac{1}{5}$
• $P(E_4) = \frac{1}{20}$
• $P(E_5) = \frac{1}{20}$
• $P(E_6) = \frac{1}{10}$

The Venn diagram shows two overlapping circles, A and B, with the following regions:

• $E_1$ and $E_2$ are in circle A.
• $E_2$ and $E_3$ are in circle B.
• $E_4$, $E_5$, $E_6$, and $E_7$ are outside both circles.

To find $P(A)$, sum the probabilities of the events within circle A:

• $P(A) = P(E_1) + P(E_2)$

Given:

• $P(E_1) = \frac{1}{5}$
• $P(E_2) = \frac{1}{5}$

So, $$P(A) = \frac{1}{5} + \frac{1}{5} = \frac{2}{5}$$

Final Answer