Answer :
To answer the question about the blood type of the patient, let's systematically examine the given table.
The patient's blood type must be one that can receive the following blood types as donors: [tex]\( O^-, O^+, B^-, B^+ \)[/tex].
Based on the table, we need to find the row where each of these donor blood types is marked with a checkmark. Let's go through each row of possible recipient blood types:
- AB+
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline AB^+ & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\ \hline \end{array} \][/tex]
AB+ can receive all donor blood types, including [tex]\( O^-, O^+, B^-, B^+ \)[/tex], so it meets the criteria.
- AB-
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline AB^- & \checkmark & & \checkmark & & \checkmark & & \checkmark & \\ \hline \end{array} \][/tex]
AB- cannot receive [tex]\( O^+ \)[/tex] and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
- A+
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline A^+ & \checkmark & \checkmark & & & \checkmark & \checkmark & & \\ \hline \end{array} \][/tex]
A+ cannot receive [tex]\( B^- \)[/tex] and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
- A-
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline A^- & \checkmark & & & & \checkmark & & & \\ \hline \end{array} \][/tex]
A- cannot receive [tex]\( O^+ \)[/tex], [tex]\( B^- \)[/tex], and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
- B+
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline B^+ & \checkmark & \checkmark & \checkmark & \checkmark & & & & \\ \hline \end{array} \][/tex]
B+ can receive [tex]\( O^- \)[/tex], [tex]\( O^+ \)[/tex], [tex]\( B^-\)[/tex], [tex]\( B^+ \)[/tex]. This meets the criteria.
- B-
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline B^- & \checkmark & & \checkmark & & & & & \\ \hline \end{array} \][/tex]
B- cannot receive [tex]\( O^+ \)[/tex] and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
- O+
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline O^+ & \checkmark & \checkmark & & & & & & \\ \hline \end{array} \][/tex]
O+ cannot receive [tex]\( B^- \)[/tex] and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
- O-
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline O^- & \checkmark & & & & & & & \\ \hline \end{array} \][/tex]
O- cannot receive [tex]\( O^+ \)[/tex], [tex]\( B^- \)[/tex], and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
From our analysis, only AB+ and B+ can receive all the specified donor blood types ([tex]\( O^-, O^+, B^-, B^+ \)[/tex]).
Since the patient can only receive from [tex]\( O^-, O^+, B^-, B^+\)[/tex], B+ would be the most likely blood type.
The patient's blood type must be one that can receive the following blood types as donors: [tex]\( O^-, O^+, B^-, B^+ \)[/tex].
Based on the table, we need to find the row where each of these donor blood types is marked with a checkmark. Let's go through each row of possible recipient blood types:
- AB+
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline AB^+ & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark & \checkmark \\ \hline \end{array} \][/tex]
AB+ can receive all donor blood types, including [tex]\( O^-, O^+, B^-, B^+ \)[/tex], so it meets the criteria.
- AB-
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline AB^- & \checkmark & & \checkmark & & \checkmark & & \checkmark & \\ \hline \end{array} \][/tex]
AB- cannot receive [tex]\( O^+ \)[/tex] and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
- A+
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline A^+ & \checkmark & \checkmark & & & \checkmark & \checkmark & & \\ \hline \end{array} \][/tex]
A+ cannot receive [tex]\( B^- \)[/tex] and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
- A-
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline A^- & \checkmark & & & & \checkmark & & & \\ \hline \end{array} \][/tex]
A- cannot receive [tex]\( O^+ \)[/tex], [tex]\( B^- \)[/tex], and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
- B+
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline B^+ & \checkmark & \checkmark & \checkmark & \checkmark & & & & \\ \hline \end{array} \][/tex]
B+ can receive [tex]\( O^- \)[/tex], [tex]\( O^+ \)[/tex], [tex]\( B^-\)[/tex], [tex]\( B^+ \)[/tex]. This meets the criteria.
- B-
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline B^- & \checkmark & & \checkmark & & & & & \\ \hline \end{array} \][/tex]
B- cannot receive [tex]\( O^+ \)[/tex] and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
- O+
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline O^+ & \checkmark & \checkmark & & & & & & \\ \hline \end{array} \][/tex]
O+ cannot receive [tex]\( B^- \)[/tex] and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
- O-
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline & O^- & O^+ & B^- & B^+ & A^- & A^+ & AB^- & AB^+ \\ \hline O^- & \checkmark & & & & & & & \\ \hline \end{array} \][/tex]
O- cannot receive [tex]\( O^+ \)[/tex], [tex]\( B^- \)[/tex], and [tex]\( B^+ \)[/tex]. This does not meet the criteria.
From our analysis, only AB+ and B+ can receive all the specified donor blood types ([tex]\( O^-, O^+, B^-, B^+ \)[/tex]).
Since the patient can only receive from [tex]\( O^-, O^+, B^-, B^+\)[/tex], B+ would be the most likely blood type.
