Question

The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11%Type B, and the rest Type AB.1.a)Someone volunteers to give blood. What is the probability that this donor1.has Type AB blood?2.has Type A or Type B?3.is not Type O?2.b)Among four potential donors, what is the probability that1.all are Type O?2.no one is Type AB?3.they are not all Type A?4.at least one person is Type B?

Answer 1

Part A

1.
`0.04`

2.
`0.51`

3.
`0.55`

Part B

1.
`0.04`

2.
`0.85`

3.
`0.97`

4.
`0.37`

Step-by-step explanation:

Given ,

Percentage of American with blood group O -
`45` %

Percentage of American with blood group A -
`40` %

Percentage of American with blood group B -
`11` %

Percentage of American with blood group AB -
`4` %

Part A

Probability that donor

1.has Type AB blood

`= 1- 0.45-0.4-0.11\\= 4`

2.has Type A or Type B

`0.4+0.11\\= 0.51`

3.is not Type O?

`1 -` Probability of type (O)

`1 - 0.45\\0.55`

Part B

1. Type O?

`0.45 * 0.45 * 0.45 * 0.45 \\= 0.04`

2.no one is Type AB?

`(1-0.04)^4\\0.96^4\\0.85`

3.they are not all Type A?

`1-(0.4)^4\\0.97`

4.at least one person is Type B?

`1- (1-0.11)^4\\1-0.63\\0.37`