# Qz 5 Solutions

```Math 200 Chp 5 Quiz
1.A random sample of 317 mp3 music players had 19 that were defective.
(a) How would you estimate the probability that a new mp3 player is defective? What is
Estimate is
&quot;*
\$&quot;(
œ &THORN;!'
(b) What is your estimate for the probability that a new mp3 player is not defective?
Estimate is &quot;  &THORN;!' œ &THORN;*%
2. If you roll a single fair die and count the number of dots on top, what is the probability
of getting a number less than 3 on a single throw?
There are two options less than 3 (&quot; and # only). Each of these has probability &quot;' .
So, we calculate...
T &ETH;rolling a &quot; OR a #) œ T &ETH;&quot;&Ntilde;  T &ETH;#&Ntilde; œ
&quot;
'

&quot;
'
œ
#
'
œ
&quot;
\$
3. You roll two fair dice, a blue one and a yellow one.
(a) Find P(even number on the blue die and 3 on the
yellow die). 3.
Since the die operate independently...
T &ETH;even on blue AND \$ on yellow&Ntilde;
œ T &ETH;even&Ntilde; T &ETH;\$&Ntilde;
œ T &ETH;# or % or '&Ntilde;T &ETH;\$&Ntilde;
œ &ETH;T &ETH;#&Ntilde;  T &ETH;%&Ntilde;  T &ETH;'&Ntilde;&Ntilde;&ETH;T &ETH;\$&Ntilde;&Ntilde;
œ &ETH; &quot;' 
&quot;
'
 &quot;' &Ntilde;&ETH; &quot;' &Ntilde;
œ &ETH; \$' &Ntilde;&ETH; &quot;' &Ntilde;
œ
\$
\$'
œ
&quot;
&quot;#
(b) Find P(3 on the blue die and even number on the yellow die).
This is just the mirror image of the event above so its probability is also
&quot;
&quot;# &THORN;
(c) Find P(even number on the blue die and even numberon the yellow die).
T &ETH;even AND even&Ntilde; œ T &ETH;even&Ntilde;T &ETH;even&Ntilde; œ &ETH; \$' &Ntilde;&ETH; \$' &Ntilde; œ
*
\$'
œ
&quot;
%
4. An urn contains 12 balls identical in every respect except color. There are 3 red balls, 7
green balls, and 2 blue balls.
(a) You draw two balls from the urn, but replace the first ball before drawing the second.
Find the probability that the first ball is red and the second is green.
Since the first ball is replaced, the draws are considered to be independent. So,...
\$
(
T &ETH;red AND then green&Ntilde; œ T &ETH;red&Ntilde;T &ETH;green&Ntilde; œ &ETH; &quot;#
&Ntilde;&ETH; &quot;#
&Ntilde;œ
#&quot;
&quot;%%
œ
(
%)
(b) Repeat part (a), but do not replace the first ball before drawing the second.
Now the draws are not independent, so we must use the formula:
T &ETH;E and F&Ntilde; œ T &ETH;E&Ntilde;T &ETH;F given E&Ntilde;
T &ETH;red AND then green&Ntilde;
œ T &ETH;red&Ntilde;T &ETH;green given red&Ntilde;
\$
(
œ &ETH; &quot;#
&Ntilde;&ETH; &quot;&quot;
&Ntilde;œ
#&quot;
&quot;\$#
œ
(
%%
5. Robert is applying for a bank loan to open up a pizza franchise. He must complete a
written application, and then be interviewed by bank officers. Past records for this bank
show that the probability of being approved on the written application is 0.63. The
probability of being approved by the interview committee is 0.85, given the candidate has
been approved on the written application. What is the probability Robert is approved on
both the written application and the interview?
Let M be the event he is approves on the interview and let [ be the even that he is
approved on the written application. Then we have...
T &ETH;[ &Ntilde; œ &THORN;'\$ and T &ETH;M given [ &Ntilde; œ &THORN;)&amp;
So,
T &ETH;[ and M &Ntilde; œ T &ETH;[ &Ntilde;T &ETH;M given [ &Ntilde; œ &ETH;&THORN;'\$&Ntilde;&ETH;&THORN;)&amp;&Ntilde; œ &THORN;&amp;\$'
```