<p>Let z be a complex solution to the equation x^2 -2x + 2 = 0. What does this equal?
A 1
B 1.41
C 2.45
D 3
E 3.73</p>
<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 all four times?
A 1/16
B 1/6
C 1/5
D 1/4
E 1/2</p>
<p>Not sure what the first question is asking… the two complex solutions to the quadratic are (1+i) and (1-i)</p>
<p>2nd question:
Sample space is
HHHH
HHHT
HHTH
HTHH
THHH</p>
<p>Thus, the chance is 1/5</p>
<p>From Number 1 is the answer A?</p>
<p>1/4 Number 2</p>
<p>No I’m pretty sure Latency’s solution is right…</p>
<p>latency’s both answers are correct.</p>
<p>Yeah…except the answer choices for the first question are a little confusing…</p>
<p>first question is weird…</p>
<p>it says X must be complex. but, choices are not complex. answer is probably A but i m not sure that this question is good-mentally-built</p>
<p>First question probably meant to ask: what is the modulus of z, which is B.</p>
<p>Sorry, guys. The question is asking for modulus of z. Can anyone break down Latency’s answer. I do not understand.</p>
<p>For q. 2, I thought since the queston said: “Given that the coins landed heads more than twice,” the probability of landing heads thrice was 1, and then the probability of landing heads four times was 1/2. Then the answer was 1/2.</p>
<p>What exactly is a complex solution though?</p>
<p>You have to incorporate all the different ways you can not get 4 heads but still get at least 3 heads. When it says that 3 heads are given, you can’t isolate the last coin flip and say 1/2 chance of HHHT and 1/2 chance of HHHH. That would imply that the problem is asking “if the first 3 out of 4 coin flips are heads, what are the chances of having all heads”. Then the answer would be 1/2. But since it is simply saying that 3 heads are given, it can be inferred that those 3 heads can come up at any point out of the 4 coin tosses.</p>
<p>Anyway, are the answers the textbook gives B and C for problems 1 and 2, respectively?</p>
<p>Apparently for number 1 it is asking for the modulus. Looked up the definition of modulus and it is as follows. In a+bi the modulus is sqrt(a^2 + b^2). So i guess the answer is just 1.41 because that is the sqrt of 1+1</p>
<p>when u try to find the solution of an eqn thru the quadratic formula and b^2-4ac is less than 0, u have a complex solution because a negativve no results in the square roots, and then uhave all this imaginary numbers</p>
<p>Thanks, Latency. I totally get it now.</p>
<p>Yeah!!! Ur answers were right. Do u have any idea of how to differentiate btw linear, quadratic, and exponential regression without using a graphing calculator</p>
<p>Yeah I know the part about a negative discriminant and stuff, but how did Latency get the complex solution as 1 when the roots are 1+i and 1-i?</p>
<p>Latency’s solution is the fastest.</p>
<p>Here’s the second side of the coin (alternate approach).</p>
<p>The formula for a conditional probability:
probability of event B provided that event A happened is
P(B|A) = P(A&B) / P(A).
It works well when both probabilities are given, for example:
in electric bulbs manufacturing 80% of bulbs pass the first test (A), 60% of bulbs pass two tests (A&B); what is the probability that a bulb which passed the first test will pass the second one (B)?
P(B|A) = .6/.8 = .75.</p>
<p>In our case with the coin flipped four times
event A is at least three heads landed,
event B is the head landed on the fourth throw,
event A&B - four heads landed,
event B|A - given that the coin landed heads up more than twice, it landed a head the fourth time.</p>
<p>P(A) = 5/16 (based on Latency’s work)
P(A&B) = 1/16
P(B|A) = (1/16) / (5/16) = 1/5.
This solution is redundant since it includes Latency’s list, but it’s a good illustration of a conditional probability.</p>
<p>I didn’t get the complex solution as 1… I didn’t know what the answer was until someone mentioned the modulus concept.</p>
<p>As for the conditional probability… euhh. Is there a logical, illustrative reason as to why that formula works? I’m trying to picture it but I’m failing.</p>