Question

the table displays the distribution of blood types a, b, ab, and o to the presence of the rh factor that is either present (pos.) or absent (neg.). use the information in the two - way table to complete the statement. the probability that a person has a positive rh factor given that he/she has type o blood is 82 percent. there is a greater probability for a person to have a than a type o blood. positive rh factor given type a blood x positive rh factor given type ab blood negative rh factor given type a blood negative rh factor given type ab blood

a b ab o total
neg. 0.07 0.02 0.01 0.08 0.18
pos. 0.33 0.09 0.03 0.37 0.82
total 0.40 0.11 0.04 0.45 1.0

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of the two - way table, if $A$ is the event of having a positive Rh factor and $B$ is the event of having type O blood, $P(A|B)=\frac{\text{Number of people with type O and positive Rh}}{\text{Total number of people with type O}}$. From the table, the proportion of people with type O and positive Rh is $0.37$ and the proportion of people with type O is $0.45$. So $P(\text{Pos}|\text{O})=\frac{0.37}{0.45}\approx 0.8222\approx 82\%$.

Step2: Calculate other conditional probabilities

• For type A blood:
• $P(\text{Pos}|\text{A})=\frac{0.33}{0.40} = 0.825$
• $P(\text{Neg}|\text{A})=\frac{0.07}{0.40}=0.175$
• For type AB blood:
• $P(\text{Pos}|\text{AB})=\frac{0.03}{0.04} = 0.75$
• $P(\text{Neg}|\text{AB})=\frac{0.01}{0.04}=0.25$

Since $0.825>0.75$, there is a greater probability for a person to have a positive Rh factor given type A blood than a positive Rh factor given type AB blood.

Answer:

The probability that a person has a positive Rh factor given that he/she has type O blood is $82$ percent. There is a greater probability for a person to have a positive Rh factor given type A blood than a positive Rh factor given type AB blood.