Questions: A blood bank catalogs the types of blood, including positive or negative Rh-factor, given by donors during the last five days. The number of donors who gave each blood is listed in the table below. Rh-factor Blood Type O A B AB Totals --------------------- O A B AB Rh-positive 150 135 37 13 335 Rh-negative 30 25 12 8 75 Totals 180 160 49 21 410 Use the following labels: Event Blood A = "selected donor has blood type A" Event Rh Negative = "selected donor has Rh-negative factor" Classify the event Blood A and event Rh Negative as: disjoint (mutually exclusive) not disjoint (not mutually exclusive)

A blood bank catalogs the types of blood, including positive or negative Rh-factor, given by donors during the last five days. The number of donors who gave each blood is listed in the table below. Rh-factor Blood Type O A B AB Totals --------------------- O A B AB Rh-positive 150 135 37 13 335 Rh-negative 30 25 12 8 75 Totals 180 160 49 21 410 Use the following labels: Event Blood A = "selected donor has blood type A" Event Rh Negative = "selected donor has Rh-negative factor" Classify the event Blood A and event Rh Negative as: disjoint (mutually exclusive) not disjoint (not mutually exclusive)
Transcript text: A blood bank catalogs the types of blood, including positive or negative Rh-factor, given by donors during the last five days. The number of donors who gave each blood is listed in the table below. \begin{tabular}{|c|c|c|c|c|c|} \hline \multirow{2}{*}{ Rh-factor } & \multicolumn{4}{|c|}{ Blood Type } & \multirow{2}{*}{ Totals } \\ \cline { 2 - 5 } & O & A & B & AB & \\ \hline Rh-positive & 150 & 135 & 37 & 13 & 335 \\ \hline Rh -negative & 30 & 25 & 12 & 8 & 75 \\ \hline Totals & 180 & 160 & 49 & 21 & 410 \\ \hline \end{tabular} Use the following labels: Event Blood A = "selected donor has blood type A" Event Rh Negative = "selected donor has Rh-negative factor" Classify the event Blood A and event Rh Negative as: disjoint (mutually exclusive) not disjoint (not mutually exclusive)
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Solution

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Solution Steps

To determine if the events "Blood A" and "Rh Negative" are disjoint (mutually exclusive) or not, we need to check if there is any overlap between the two events. Specifically, we need to see if there are any donors who have both blood type A and an Rh-negative factor.

Solution Approach
  1. Check the number of donors who have blood type A and an Rh-negative factor.
  2. If the number is greater than zero, the events are not disjoint.
  3. If the number is zero, the events are disjoint.
Step 1: Identify the Events

We are given two events:

  • Event Blood A: The selected donor has blood type A.
  • Event Rh Negative: The selected donor has an Rh-negative factor.
Step 2: Determine Overlap

From the data, the number of donors who have both blood type A and an Rh-negative factor is \( 25 \).

Step 3: Classify the Events

Since the number of donors with both characteristics is greater than zero, the events are classified as not disjoint (not mutually exclusive).

Final Answer

The events Blood A and Rh Negative are \(\boxed{\text{not disjoint (not mutually exclusive)}}\).

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