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 person to have a positive rh factor given type o blood.

	a	b	ab	o	total
pos.	.33	.09	.03	.37	.82
total	.40	.11	.04	.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 terms of the table, if $A$ is the event of having a positive Rh - factor and $B$ is the event of having type O blood, then $P(A|B)=\frac{\text{Number of people with type O and positive Rh}}{\text{Number of people with type O}}$.

Step2: Identify values from the table

The number of people with type O and positive Rh is $0.37$, and the number of people with type O is $0.45$.

Step3: Calculate the conditional probability

$P(\text{Pos}|\text{O})=\frac{0.37}{0.45}\approx 0.8222$. To convert to a percentage, we multiply by 100: $0.8222\times100 = 82.22\%$.

Answer:

$82.22$