Question

United Blood Services is a blood bank that serves more than $500$hospitals in $18$ 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 $43\%$ of people have type O blood and $15\%$ of people haveRh- factor; $52\%$of people have type O or Rh- factor.

a. Find the probability that a person has both typeO blood and the Rh- factor.

b. Find the probability that a person does NOT have both type O blood and the Rh- factor

Short answer

(a) The probability that a person has both type O blood and the Rh-factor is $0.06$.

(b) The probability that a person does not have both type O blood and the Rh-factor is$0.94$.

Step-by-step solution

Given information (part a)

United blood services is a blood bank that serves more than $500$hospitals in $18$ 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 $43\%$ of people have type O blood and $15\%$ of people have Rh-factor; $52\%$of people have type O or Rh-factor.

Explanation (part a)

Let the events be

$\text{B}=$Event that person has type O blood

$R=$Event that a person have Rh-factor

We have

$$\begin{gathered} P\left(B\right)=0.43 \\ P\left(R\right)=0.15 \\ P\left(BorR\right)=0.52 \end{gathered}$$

We need to calculate the probability that a person has both type O blood and the Rh-factor

Thus is given as $P\left(BandR\right)$

$$\begin{gathered} P\left(BorR\right)=P\left(B\right)+P\left(R\right)-P\left(BandR\right) \\ P\left(BandR\right)=P\left(BorR\right)-\left[P\left(B\right)+P\left(R\right)\right] \end{gathered}$$

Substituting the values, we get

$$\begin{gathered} P\left(BorR\right)=0.52-\left[0.43+0.15\right] \\ P\left(BandR\right)=0.06 \end{gathered}$$

Given information (part b)

United blood services is a blood bank that serves more than $500$hospitals in $18$ states. According to their website, a person with type Oblood and a negative Rh factor(Rh-) can donate blood to any person with any blood type. Their data show that $43\%$ of people have type O blood and $15\%$ of people have Rh-factor; $52\%$ of people have typeO or Rh-factor.

Explanation (part b)

Let the events be

$\text{B}=$Event that person has type O blood

$\text{R}=$Event that a person have Rh-factor

We have

$$\begin{gathered} P\left(B\right)=0.43 \\ P\left(R\right)=0.15 \\ P\left(BandR\right)=0.06 \end{gathered}$$

We need to calculate the probability that a person has both type O blood and the Rh-factor

Thus is given as $P\left(BandR\right)\text{'}$

$P\left(BandR\right)\text{'}=1-P\left(BandR\right)$

Substituting the values, we get

$$\begin{gathered} P\left(BandR\right)\text{'}=1-0.06 \\ P\left(BandR\right)\text{'}=0.94 \end{gathered}$$