Let A1 and A2 be the events that a person is lefteye

Chapter 1, Problem 3E

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QUESTION:

Let \(A_{1}\) and \(A_{2}\) be the events that a person is left eye dominant or right-eye dominant, respectively. When a person folds his or her hands, let \(B_{1}\) and \(B_{2}\) be the events that the left thumb and right thumb, respectively, are on top. A survey in one statistics class yielded the following table:

If a student is selected randomly, find the following probabilities: (a) \(P\left(A_{1} \cap B_{1}\right)\), (b) \(P\left(A_{1} \cup B_{1}\right)\), (c) \(P\left(A_{1} \mid B_{1}\right)\), (d) \(P\left(B_{2} \mid A_{2}\right)\). (e) If the students had their hands folded and you hoped to select a right-eye-dominant student, would you select a "right thumb on top" or a "left thumb on top" student? Why?

Equation Transcription:

 

 

Text Transcription:

A_1  

A_2  

B_1  

B_2  

P(A_1 cap B_1)  

P(A_1 cup B_1)

P(A_1∣B_1)  

P(B_2∣A_2)

Questions & Answers

QUESTION:

Let \(A_{1}\) and \(A_{2}\) be the events that a person is left eye dominant or right-eye dominant, respectively. When a person folds his or her hands, let \(B_{1}\) and \(B_{2}\) be the events that the left thumb and right thumb, respectively, are on top. A survey in one statistics class yielded the following table:

If a student is selected randomly, find the following probabilities: (a) \(P\left(A_{1} \cap B_{1}\right)\), (b) \(P\left(A_{1} \cup B_{1}\right)\), (c) \(P\left(A_{1} \mid B_{1}\right)\), (d) \(P\left(B_{2} \mid A_{2}\right)\). (e) If the students had their hands folded and you hoped to select a right-eye-dominant student, would you select a "right thumb on top" or a "left thumb on top" student? Why?

Equation Transcription:

 

 

Text Transcription:

A_1  

A_2  

B_1  

B_2  

P(A_1 cap B_1)  

P(A_1 cup B_1)

P(A_1∣B_1)  

P(B_2∣A_2)

ANSWER:

Step 1 of 6:

Given that a survey is conducted taking into consideration 35 respondents. The event A1 is defined as the person is left eye dominant and A2 is defined as the person is right eye dominated.

The event B1 is defined as left thumb is on the top when hand is folded and event B2 is defined as right thumb is on the top when hand is folded.

Also the outcomes of the survey are a3.png


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