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AP2.23. There are four major blood types in humans: O,A,B, and AB. In a study conducted using blood specimens from the Blood Bank of Hawaii, individuals were classified according to blood type and ethnic group. The ethnic groups were Hawaiian, Hawaiian-White, HawaiianChinese, and White. Suppose that a blood bank specimen is selected at random.

(a) Find the probability that the specimen contains type O blood or comes from the Hawaiian-Chinese ethnic group. Show your work.

(b) What is the probability that the specimen contains type AB blood, given that it comes from the Hawaiian ethnic group? Show your work.

(c) Are the events "type B blood" and "Hawaiian ethnic group鈥 independent? Give appropriate statistical evidence to support your answer.

Now suppose that two blood bank specimens are selected at random.

(d) Find the probability that at least one of the specimens contains type A blood from the White ethnic group.

Short Answer

Expert verified

a). The required probability is0.4516.

b). The required probability is 0.0212.

c). They are not independent.

d). The required probability is0.5706.

Step by step solution

01

Part (a) Step 1: Given Information

Given data,

02

Part (a) Step 2: Explanation

To find the probability that the specimen contains type O blood or comes from the Hawaiian-Chinese ethnic group, that

P(OHC)=P(O)+P(HC)-P(OHC)

=62337145057+5385145057-2206145057

=0.4297+0.03712-0.0152

=0.4516

03

Part (b) Step 1: Given Information

Given data:

04

Part (b) Step 2: Explanation

To determine the probability that the samples include type blood AB, assuming that it is from the Hawaiian ethnic group,

P(ABH)=P(HAB)P(H)

=991903+2490+178+99

=0.0212

05

Part (c) Step 1: Given Information

Given data,

06

Part (c) Step 2: Explanation

The probability of having the blood group Bis therefore,

P(B)=17604145057

=0.1214

The probability of Hawaiians having blood group B is as follows:

P(BHawaiian)=1784670

=0.0381

If the two events are independent, their probabilities should be equal. Because the two probability aren't equal, the occurrences "having blood type B" and "Hawaiian ethnic group" aren't mutually exclusive.

07

Part (d) Step 1: Given Information

Given data:

08

Part (d) Step 2: Explanation

The chance of not obtaining an A from Wis the complement of getting an A from Won the first draw, with a total population of 145057.

1-50008145057

=0.6553

Given that A did not come from W in the initial draw, there are 145057persons left, with 50008in the A and W group. Because the population was so huge, these two odds are nearly equal.

1-50008145057

localid="1652866656927" =0.6553

Use the multiplication rule, as follows, to get the likelihood of both events happening.

localid="1653040234665" P(None)=0.65532

=0.4294

We have,

P(1)=1-P(None)

localid="1652866823781" =1-0.429

=0.5706

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