Question

determining conditional probabilities of blood types
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 percent.
there is a greater probability for a person to have a
than a
type o blood.
positive rh factor given type a blood
positive rh factor given type ab blood
negative rh factor given type a blood
negative rh factor given type ab blood

Explanation:

Step1: Calculate conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Here, \(A\) is "positive Rh factor" and \(B\) is "type O blood". \(P(A\cap B) = 0.37\) (from the table, Pos. and O cell), \(P(B)=0.45\) (total for O). So \(P=\frac{0.37}{0.45}\).

Step2: Convert to percentage

\(\frac{0.37}{0.45}\approx0.8222\), and \(0.8222\times100 = 82.22\%\) (rounded to two decimal places).

For the second part:

Step1: Calculate probabilities

• Positive Rh factor given type A blood: \(P=\frac{0.33}{0.40}=0.825\)
• Positive Rh factor given type AB blood: \(P=\frac{0.03}{0.04} = 0.75\)
• Negative Rh factor given type A blood: \(P=\frac{0.07}{0.40}=0.175\)
• Negative Rh factor given type AB blood: \(P=\frac{0.01}{0.04}=0.25\)

Since \(0.825>0.8222\) (the probability of positive Rh factor given type O blood), the first blank is filled with positive Rh factor given type A blood.

Answer:

The probability that a person has a positive Rh factor given that he/she has type O blood is \(82.22\) percent. There is a greater probability for a person to have a positive Rh factor given type A blood than a type O blood.