Question

8. If one has a fair coin, it is easy to generate a random number in {0, 1} with equal probability: e.g., one simply flips this coin and assign 0 to a Head and 1 to a T ail. How do you generate such a random number if you are given a coin with unknown bias?

9. A novel type of bacteria is found in a recent medical research. After every minute, the bacteria may die, or stay the same, or split into two or split into three with equal probability 1/4. All its offspring, if any, behave the same independently. Suppose there is only one bacteria in the petri dish, what is the probability that the bacteria population will die out.

Answer 1

8) In case of biased coin prob of head = p and prob of tail =(1-p)

so prob of HT = p(1-p)

and prob of TH =(1-p)p

which are equal so we can repeat the experiment and assign 1 when HT occurs and 0 when TH occurs and ignore the event when HH or TT occurs.

This will result in random number generation {0,1}

9)