Gene Expression. In studies of the human genome, gene expression levels are ofte

Question

Gene Expression. In studies of the human genome, gene expression levels are often studied to investigate patterns that might identify certain diseases. Consider three different genes A, B, and C that have the potential to cause cancer (called oncogenes). In a sample of cancer patients it was found that:

60% have high expression of gene A, 40% have high expression of gene B, and 25% have high expression of gene C

70% have high expression of A or B (or both), 69% have high expression of A or C (or both), and 52% have high expression of both B or C (or both)

8% have high expression of all three genes

Find the probability that a randomly selected cancer patient.

a. Has high expression in both genes A and B.

b. Has high expression in both genes A and B, but not C.

c. Has high expression in at most two genes.

Explanation / Answer

a. P(A)-P(B)-P(AuB)=0.60+0.40-0.70=0.3

b.a-P(C)=0.3-0.25=0.05

c. we will first find P(AnC) and P(BnC)

P(AnC)=P(A)+P(C)-P(AuC)=0.6+0.25-0.69=0.16

P(BnC)=P(B)+P(C)-P(BuC)=0.4+0.25-0.52=0.13

required probability =0.3+0.16+0.13=0.59

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