Question

H60 (with probabilities of coming up heads 0.5, 0.55, and 0.6 respectively). You take one coin and flip it 10 times. It lands heads 9 times. How likely is the coin to be of each possible type?

Answer 1

Here the concept of bayes theorem will be used.

A jar is equally populated with coins of type H50, H55, and H60.

This means P(getting coin H50)=$\frac{1}{3}$

P(getting coin H55)=$\frac{1}{3}$

P(getting coin H60)=$\frac{1}{3}$

Also one needs to know the pdf of binomail distribution.

If X~Binomial(n, p)

where n=total number of trials

p=probability of success

then

P(X=r) = $\binom{n}{r} p^{r}(1-p)^{n-r}$ r=0,1,2,....n

= 0 otherwise

= 0.04。310784 xt 6 01432992488 Hence, the possibiiy that Coin wj) be ot type H50 given thot 9 heads resulted IS 0.22וד61577 The possibilih hot the coin is of type H55 given thou the Rip resulted in 9 heads The possibility tha the coin.is of type H6o given thot the Aip resulted in g hea ds is PCA3 /B) 2907668186