Section 4.5 Learning Check||Please enter your Full Name:|Your Email Address:|Your ID Number or Password:|Suppose that A and B are two independent events with P(A)=0.2 and P(B)=0.4. P(A or B) is # 0.08 %% 0.12 %% 0.52 %% 0.40 %%|Event A occurs with probability 0.8. The probability that event B occurs given that A occurs is 0.5. The probability that both A and B occur is # 0.3 %% 0.4 %% 0.8 %% cannot be determined %%|Event A occurs with probability 0.3 and event B occurs with probability 0.4. If A and B are independent, we may conclude # P(A and B)=0.12 %% P(A&KPHHASH124;B)=0.3 %% P(B&KPHHASH124;A)=0.4 %% all of the above %%|There is a 0.20 chance that a college student will go to a graduate school. If s&#124;he goes to a graduate school with probability 0.7, s&#124;he will have the life style that s&#124;he wants. If s&#124;he does not go to a graduate school, her&#124;his chance is 0.4. # The probability tree that describes this problem is&lt;br&gt;&lt;img src=&quot;treea.jpg&quot;&gt; %% The probability tree that describes this problem is&lt;br&gt;&lt;img src=&quot;treeb.jpg&quot;&gt; %% The probability tree that describes this problem is&lt;br&gt;&lt;img src=&quot;treec.jpg&quot;&gt; %% The probability tree that describes this problem is&lt;br&gt;&lt;img src=&quot;treed.jpg&quot;&gt; %%|Consider the following probability tree. <br><img src="tree5.jpg"><br>P(A and B) is # 0.67 %% 0.50 %% 0.40 %% 0.04 %%|Consider the following probability tree. <br><img src="tree5.jpg"><br>P(B) is # 0.04 %% 0.20 %% 0.40 %% 0.22 %%|Consider the following probability tree. <br><img src="tree5.jpg"><br>P(B&#124;A) is # 0.04 %% 0.18 %% 0.20 %% 0.40 %%|Consider the following probability tree. <br><img src="tree5.jpg"><br>P(A&#124;B) is # 0.04 %% 0.18 %% 0.20 %% 0.40 %%