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Answer:
(a) 0.1719
(b) 0.3504
Step-by-step explanation:
For every coin the number of heads follows a Binomial distribution and the probability that x of the 10 times are heads is equal to:
Where n is 10 and p is the probability to get head. it means that p is equal to 0.5 for the fair coin and 0.3 for the biased coin
So, for the fair coin, the probability that the number of heads is less than 4 is:
Where, for example, P(0) and P(1) are calculated as:
Then, , so there is a probability of 0.1719 that you conclude that the coin is biased given that the coin is fair.
At the same way, for the biased coin, the probability that the number of heads is at least 4 is:
Where, for example, P(4) is calculated as:
Then, , so there is a probability of 0.3504 that you conclude that the coin is fair given that the coin is biased.