Question 1209842
.
4.24. There are two urns containing pens and pencils. Urn #1 contains three
pens and seven pencils and Urn #2 contains eight pens and four pencils.
(a) An urn is chosen at random and an object is drawn. What is the proba-
bility that it is a pencil?
(b) An urn is chosen at random and an object is drawn. If the object drawn
is a pencil, what is the probability that it came from Urn #1?
(c) If an urn is chosen at random and two objects are drawn simultaneously <U>from this urn</U>,
what is the probability that both are pencils?
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I edited your post to make the problem as clear as it should be.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;My editing is underlined.



<pre>
(a)  P(a) = {{{(1/2)*(7/10)}}} + {{{(1/2)*(4/12)}}} = {{{7/20}}} + {{{4/24}}} = {{{42/120}}} + {{{20/120}}} = {{{62/120}}} = {{{31/60}}}.



(b)  P(b) = {{{7/(7+4)}}} = {{{7/11}}}.



(c)  P(c) = {{{(1/2)*(7/10)*(6/9)}}} + {{{(1/2)*(4/12)*(3/11)}}} = {{{(7/10)*(1/3)}}} + {{{(1/6)*(3/11)}}} = {{{7/30}}} + {{{3/66}}} = {{{7/30}}} + {{{1/22}}} = {{{(7*22+30)/(30*22)}}} = {{{184/(30*22)}}} = {{{46/165}}}.
</pre>

Solved.