Questions: United Blood Services is a blood bank that serves more than 325 hospitals in 15 states. According to their website, a person with type O blood and a negative Rh factor (Rh-) can donate blood to any person with any blood type. Their data show that 42% of people have type O blood and 15% of people have Rh- factor; 43% of people have type O or Rh - factor. Enter decimal answers rounded to 4 places where possible. a. Find the probability that a person has both type O blood and the Rh-factor. b. Find the probability that a person does NOT have both type O blood and the Rh- factor.

United Blood Services is a blood bank that serves more than 325 hospitals in 15 states. According to their website, a person with type O blood and a negative Rh factor (Rh-) can donate blood to any person with any blood type.

Their data show that 42% of people have type O blood and 15% of people have Rh- factor; 43% of people have type O or Rh - factor.

Enter decimal answers rounded to 4 places where possible.
a. Find the probability that a person has both type O blood and the Rh-factor.
b. Find the probability that a person does NOT have both type O blood and the Rh- factor.

Transcript text: United Blood Services is a blood bank that serves more than 325 hospitals in 15 states. According to their website, a person with type O blood and a negative Rh factor (Rh-) can donate blood to any person with any blood type. Their data show that $42 \%$ of people have type O blood and $15 \%$ of people have Rh- factor; $43 \%$ of people have type O or Rh - factor. Enter decimal answers rounded to 4 places where possible. a. Find the probability that a person has both type O blood and the Rh-factor. $\square$ b. Find the probability that a person does NOT have both type O blood and the Rh- factor. $\square$

Solution

Solution Steps

To solve these probability questions, we can use the principle of inclusion-exclusion.

a. To find the probability that a person has both type O blood and the Rh- factor, we use the formula for the intersection of two events: P(O and Rh-) = P(O) + P(Rh-) - P(O or Rh-).

b. To find the probability that a person does NOT have both type O blood and the Rh- factor, we subtract the probability found in part (a) from 1.

Step 1: Given Probabilities

We are provided with the following probabilities:

$ P(O) = 0.42 $ (the probability of having type O blood)
$ P(Rh-) = 0.15 $ (the probability of having the Rh- factor)
$ P(O \cup Rh-) = 0.43 $ (the probability of having either type O blood or the Rh- factor)

Step 2: Calculate Probability of Both Events

To find the probability that a person has both type O blood and the Rh- factor, we use the formula for the intersection of two events: \[ P(O \cap Rh-) = P(O) + P(Rh-) - P(O \cup Rh-) \] Substituting the values: \[ P(O \cap Rh-) = 0.42 + 0.15 - 0.43 = 0.14 \]

Step 3: Calculate Probability of Not Having Both Events

To find the probability that a person does NOT have both type O blood and the Rh- factor, we subtract the probability found in Step 2 from 1: \[ P(\text{not } (O \cap Rh-)) = 1 - P(O \cap Rh-) = 1 - 0.14 = 0.86 \]