A box contains two coins a regular coin and one two headed...

A box contains two coins: a regular coin and one two-headed coin. I choose a coin at random and toss it twice. Define the following events. A = First toss results in a H B = Second toss results in a H C = Regular coin has been selected Are A and B independent? Are A and B conditionally independent given C? Find P(A|C), P(B|C), P(A∩B|C), P(A), P(B), and P(A∩B), and use them to answer the question.

Transcript

00:01 Okay, so we have two coins that we are picking from, and the first coin just has a head and a tail, and the other has a head in the head.

00:10 So if you think of it, you really have like four possibilities for the first coin toss, right? you could get a head from this coin or a tail from this coin, or this head from this coin, or this head from this coin.

00:24 So we know that we're calling a means that the first tosses ahead.

00:30 B is that the second tosses ahead, and c is that i have the regular coin.

00:40 So we're trying to see if a and b are independent.

00:43 First of all, we have to find some probabilities.

00:45 So the probability of a given c, or the probability that if i have a regular coin, i get ahead on the first, is just one half.

00:55 Right.

00:56 Same with the probability of b given c, the probability of getting head on the second one, if i am looking at the regular coin or given c is also 0 .5.

01:08 The probability of a and b given c, or in other words, the probability of getting two heads in a row if i'm looking at the regular coin is just going to be 1 fourths, right, 0 .5 times 0 .5.

01:24 Probability of a, which is getting the first one being a head.

01:31 One way to look at it is just like i said before right we have four possibilities for that first that first coin flip and 75 % of them are getting heads and that's the same thing with b okay and then the probability of a and b is equal to okay so we have two coins that we are picking from so that equals the probability of a the probability of b given a is one way to think about it.

02:18 Or one way to also think about it is just like with a stem diagram...

Question

Please give Ace some feedback