Math II, probability help!

Test Preparation SAT Subject Test Preparation
1

<p>Hi, whenever I take a practice test, I am usually stumped at the ones with coin toss probability. Are there any complicated probability questions on the test?</p>

<p>Here is one from sparknotes that even the explanation was giving me a hard time:</p>

<ol>
<li><pre><code>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?
</code></pre>

<p>(A) 1/16
(B) 1/6
(C) 1/5
(D) 1/4
(E) 1/2</p></li>
</ol>

<p>Can someone please explain why the answer is C?
Thank you!</p>

2

<p>I will copy and paste the answer found in this topic:</p>

<p><a href=“http://talk.collegeconfidential.com/sat-subject-tests-preparation/815422-sparknotes-practice-tests-math-2-physics.html[/url]”>http://talk.collegeconfidential.com/sat-subject-tests-preparation/815422-sparknotes-practice-tests-math-2-physics.html&lt;/a&gt;&lt;/p&gt;

<p>“There are only four flips, so it is easier just to write out the possibilities with more than two heads (H for heads, T for tails). There are only 5: HHHT, HHTH, HTHH, THHH, and HHHH. We are looking for probability of HHHH, which is one out of five.”</p>

<p>:)</p>

3

<p>We know the the coin landed heads more than twice.</p>

<p>There were 4 flips.</p>

<p>So either we had 3 heads, or 4 heads.</p>

<p>3 heads can be achieved in four ways. HHHT HHTH HTHH THHH</p>

<p>4 heads in only 1 way: HHHH</p>

<p>So, out of total 5 cases, only in one we have four heads.</p>

<p>Probability: 1/5</p>