Suppose that start-up companies in the area of biotechnology have probability of

Question

Suppose that start-up companies in the area of biotechnology have probability of 0.2 of becoming profitable and that those in area of information technology have probability to 0.15 of becoming profitable. A venture capitalist invests in one firm for each type. Assume the companies function independently. What is the probability that neither company become profitable? What is the probability that at least one of the two companies become profitable? A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. What is probability that a in randomly sampled individual, gene 1 is dominant. If in a randomly sampled individual, gen 1 is recessive, what is the probability the gene 2 is also recessive.

Explanation / Answer

2. a. P(Both not profitable) = (1-0.20) * (1-0.15) = 0.8 * 0.85 = 0.68

b. P(at least one profitable) = 1 - P(Both not profitable) = 1 - 0.68 = 0.32

3. a. P(gene 1 is dominant) = (56+24) / (100 = 0.80

b. P(gene 2 recessive | gene 1 recessive) = P(gene 2 recessive and gene 1 recessive) / P(gene 2 recessive)

= 6 / (100) / [ (24+6)/100] = 6 / 30 = 0.20

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