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1. Human blood may contain either or both of 2 antigens, A & B. Blood containing only the A antigen is called type A. Blood containing only the B antigen is called type B. Type AB contain both type A & B antigens. Blood that contains neither antigen is called type O. A certain bloodbank has blood from a total of 1200 donors. Of these, 570 have type O, 440 have type A and 12have type B blood. How many donors have type AB blood?. What is the probability that a randomly selected donor is type O. A recipient with type A blood may safely receive blood from a donor whose blood does no contain the B antigen. What is the probability that a randomly chosen blood donor may donate to a recipient with type A blood?

Sagot :

Answer:

Total number of donors:

Total donors

=

1200

Total donors=1200

Blood types:

Type O: 570 donors

Type A: 440 donors

Type B: 12 donors

Type AB: unknown (let's denote it as

x)

Finding the number of AB donors:

The total number of donors should be equal to the sum of donors of all blood types:

570

(

O

)

+

440

(

A

)

+

12

(

B

)

+

(

AB

)

=

1200

570(O)+440(A)+12(B)+x(AB)=1200

So, we can solve for

x:

570

+

440

+

12

+

=

1200

570+440+12+x=1200

1022

+

=

1200

1022+x=1200

=

1200

−

1022

x=1200−1022

=

178

x=178

Thus, the number of donors with type AB blood is 178.

Probability that a randomly selected donor is type O:

(

Type O

)

=

Number of type O donors

Total number of donors

=

570

1200

=

19

40

≈

0.475

P(Type O)=

Total number of donors

Number of type O donors

​

=

1200

570

​

=

40

19

​

≈0.475

Probability that a randomly chosen donor may donate to a recipient with type A blood:

A recipient with type A blood can receive blood from donors with type A or type O blood.

So, the total number of donors that can donate to a type A recipient is:

Number of type A donors

+

Number of type O donors

=

440

+

570

=

1010

Number of type A donors+Number of type O donors=440+570=1010

Therefore, the probability is:

(

Donor for Type A recipient

)

=

1010

1200

=

101

120

≈

0.8417

P(Donor for Type A recipient)=

1200

1010

​

=

120

101

​

≈0.8417

Summary:

The number of donors with type AB blood is 178.

The probability that a randomly selected donor is type O is 0.475.

The probability that a randomly chosen blood donor may donate to a recipient with type A blood is approximately 0.8417.

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