Question

1. - / 14 points

a random sample of people was taken and their blood types were recorded. the table below shows the probabilities of blood types from that sample.
(a) fill in the missing blanks in the table.

	a	b	ab	o	total
rh+	0.31	0.11	0.04	0.39
rh-	0.05	0.02	0.01
total

(b) what is the probability a person will have type o blood?
(c) what is the probability a person will be rh- given he or she has type a blood? (give your answer to 4 decimals.)
(d) what is the probability a person will have type b blood given that he or she is rh+? (give your answer to 4 decimals.)
(e) what is the probability that a married couple will both be rh-? (give your answer to 4 decimals.)
hint: are each partners blood type independent?
(f) what is the probability that a married couple will both have type a blood? (give your answer to 4 decimals.)
(g) what is the probability that at least one partner in a married couple will have type ab blood? (give your answer to 4 decimals.)

Explanation:

Part (a)

Step 1: Calculate Rh+ Total

Sum the probabilities for Rh+: \( 0.31 + 0.11 + 0.04 + 0.39 = 0.85 \)

Step 2: Calculate Rh- O

First, find Rh- total. The grand total should be 1. So Rh- total is \( 1 - 0.85 = 0.15 \). Then, Rh- O is \( 0.15 - (0.05 + 0.02 + 0.01) = 0.07 \)

Step 3: Calculate Rh- Total

As above, \( 0.05 + 0.02 + 0.01 + 0.07 = 0.15 \)

Step 4: Calculate A Total

\( 0.31 + 0.05 = 0.36 \)

Step 5: Calculate B Total

\( 0.11 + 0.02 = 0.13 \)

Step 6: Calculate AB Total

\( 0.04 + 0.01 = 0.05 \)

Step 7: Calculate O Total

\( 0.39 + 0.07 = 0.46 \)

Step 8: Grand Total

\( 0.85 + 0.15 = 1 \) (or sum of totals: \( 0.36 + 0.13 + 0.05 + 0.46 = 1 \))

Filled table:

	A	B	AB	O	Total
Rh-	0.05	0.02	0.01	0.07	0.15
Total	0.36	0.13	0.05	0.46	1.00

Part (b)

Step 1: Probability of O blood

From the total row, O total is \( 0.39 + 0.07 = 0.46 \)

Answer:

\( 0.46 \)

Part (c)

Step 1: Use Conditional Probability Formula

\( P(\text{Rh-} | \text{A}) = \frac{P(\text{Rh- and A})}{P(\text{A})} \)
\( P(\text{Rh- and A}) = 0.05 \), \( P(\text{A}) = 0.36 \)

Step 2: Calculate the Probability

\( \frac{0.05}{0.36} \approx 0.1389 \)