<p>A two-sided coin is flipped four times. Given that the coin landed heads up more than twice, what is the probability that it landed heads up all four times?</p>
<p>a) 1/16
b) 1/6
c) 1/5
d) 1/4
e) 1/2</p>
<p>E?<br>
Because if you're already given that the coin has landed heads up at least 3 times, then there is only one flip that counts.</p>
<p>No, the right answer is c for some reason...</p>
<p>Yeah, it seems like since its given that it landed heads up more than two times, it either landed up three times of four times. The probability it landed heads up three times is (1/4 or 4/16) and four times is (1/16). Maybe if you take it as there is a 4/16 chance it was three times and a 1/16 chance it was 4 times, there is a 1 in 5 chance that it was 3 times.</p>
<p>Does that make sense?</p>
<p>Reviving this one from the dead. Could someone please explain this to me? I don't quite comprehend...</p>
<p>well "conditional probability" has a specific formula.. you can google it
But prob B given A is P (B ㅣA) = P(B^A)/P(A) (^: intersection)
now P(A) is 3 or 4 times so 5/16
P(B^A) is same as 4 times or P(B) as the intersection of 4 times and at least 3 times is 4 times.
So then P (B^A) is 1/16</p>
<p>therefore, plugging it into the formula, you get 1/5
Get it?</p>
<p>Kind of. Yeah. That plus a little messing around on my own helped. Thanks!</p>
<p>Yea, I'm sure "using the formula" isn't always a quick way or easier way, but that at least works for me..
Are you a junior by the way? just curious...</p>
<p>Yup (10 char)</p>
<p>You don't need a formula...its intuitive. you know that it landed heads more than 2 times. Therefore, there are two main possibilities: It landed heads 3 times and it landed heads all 4 times. The former has four subcategories, since the one tail could occur at any of the 4 positions (1st, 2nd, 3rd, or 4th) and the latter has only one (all heads). 4+1=5 total possible outcomes. Landing heads all four times is one of these 5 possible outcomes, therefore there is a 1/5 chance.</p>
<p>There are sixteen possible results of the four coin flips. Since we know that we got at least three heads, these are the five results that remain after eliminating the impossible ones:</p>
<p>HHHH HHHT HHTH HTHH THHH</p>
<p>All five are equally likely. One of the five has all heads. So, probability is one in five, or 1/5.</p>