Question

1. a) If a radioactive substance has a half-life of one year, does this mean that it will be completely decayed after two years? Explain

    b) Many individuals carry recessive gene for albinism but they are not albino unless they recieve the gene from both their parents. In the U.S., an individual`s probability of recieving the gene from a given parent is about 0.014. What is the probability that a given child will be born albino?

   c) Devise a method for testing experimentally the hypothesis that a gambler`s chance of winning at craps is independent of her previous record of win and losses. if you dont invoke the mathematical definition of statistical independence, then you haven`t propose a test. This has nothing to do with the details of the rules of craps, or with the fact that it`s a game played using dice.

Answer 1

Problem -1

Half life:- The time taken for the radioactivity of a specified isotope to fall to half its original value.

So if the half life of a substance is one year, that means it decays half of its initial value by the end of one year. Now in the next year it decays the half of the earlier remaining quantitiy which means after two years it 1/4th of the original quantity remains.

This process continuously going on to the infinite time which means the radioacitve substances tends to become zero but actually they never completely vanished. The graph of decay is shown below.

After infinite time the radio active substance will become zero and infinite is not defined.