# Question: We are in possession of two coins one which is

We are in possession of two coins, one which is fairly balanced and turns up heads with probability 1/ 2, the other is weighted such that heads shows up with probability 3/ 4 and tails with probability 1/ 4. The two coins are identical looking and feeling so we cannot tell which is which. In order to determine which the biased coin is we toss the coin 10 times and observe the number of heads that occurred.

(a) If 7 heads were observed, what is the probability that the coin flipped was the fair coin?

(b) If 3 heads were observed, what is the probability that the coin flipped was the fair coin?

(a) If 7 heads were observed, what is the probability that the coin flipped was the fair coin?

(b) If 3 heads were observed, what is the probability that the coin flipped was the fair coin?

**View Solution:**## Answer to relevant Questions

Researchers are investigating the physical development of children over time. In the study, children are given a physical aptitude test at several stages in their development. Let be the event that the child passes the ...If two events A and B are such that Pr(A) is not zero and Pr(B) is not zero, what combinations of independent (I ), not independent (NI ), mutually exclusive (M), and not mutually exclusive (NM) are permissible? In other ...Suppose the arrival of telephone calls at a switch can be modeled with a Poisson PMF. That is, if X is the number of calls that arrive in t minutes, then Where λ is the average arrival rate in calls/ minute. Suppose that ...An experiment consists of rolling a pair of (six- sided) dice and observing the sum. This experiment is repeated until the sum of 7 is observed at which point the experiment stops. Let be the random variable which represents ...Develop a careful proof of Theoram 2.1 which states that for any events A and B, Pr (A U B) = Pr (A) + Pr (B) – Pr (A ∩ B). One way to approach this proof is to start by showing that the set can be written as the union ...Post your question