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  4. Cystic fibrosis is an autosomal recessive disease. In an island having a population of 200 people, 98 people suffer from cystic fibrosis. How many people are carriers of this disease?

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Q. Cystic fibrosis is an autosomal recessive disease. In an island having a population of 200 people, 98 people suffer from cystic fibrosis. How many people are carriers of this disease?

NTA AbhyasNTA Abhyas 2020Evolution

Solution:

Cystic fibrosis is caused due to a recessive gene. Individuals suffering from this disease are homozygous recessive. Applying Hardy Weinberg's equation here, $q^{2}=\frac{98}{200} \, =0.49$ . Hence, $q=0.7$ . Thus $p=1 \, -q=0.3.$
If the carrier of this disease is heterozygous individuals. Their proportion will be $2pq \, = \, 2\times \, 0.7\times \, 0.3 \, = \, 0.42$ . In this population, carriers will be $0.42\times 200 \, = \, 84.$