S.O.S. Mathematics CyberBoard

1.
A bag contains printed articles of 4 different kinds: periodicals, novellas, newspapers and notebooks. When 4 articles are drawn from the bag without replacement, the following events are equally likely:
the selection of 4 periodicals
the selection of 1 novella and 3 periodicals
the selection of 1 newspaper, 1 novella and 2 periodicals and
the selection of 1 article of each kind
What is the smallest number of articles in the bag satisfying these conditions?


A. 19


B. 18


C. 21


D. More than 46


E. 46


2. The figure below is the map of a part of a city. The small rectangles are blocks and the spaces in between are streets. Each morning, a student walks from intersection A to intersection B along the streets shown and always walking east or south. For variety, at each intersection where he has a choice, he tosses a fair coin and goes east if it comes up heads and south otherwise. What is the probability that on any given morning, he walks through intersection c?

A. 1/2
B. 4/7
C. 11/32
D. 5/16
E. 21/32

Are you able to answer this simpler version:

A bag contains printed articles of 2 different kinds: periodicals and novellas.
When 4 articles are drawn from the bag without replacement,
the following events are equally likely:
the selection of 4 periodicals
the selection of 1 novella and 3 periodicals
What is the smallest number of articles in the bag satisfying these conditions?

If not, you need help from your teacher...

_________________
Walked over to a beggar...he gave me a quarter...

1st:
we have a - periodicals
b - novellas
c - newspapers
d - notebooks

if P( drawn 4 periodicals) = P(drawn 1 novella and 3 periodicals) -> b = a - 3 (prove it)
P (drawn 1 novella and 3 periodicals) = P(drawn 1 newspaper, 1 novella and 2 periodicals) -> c = a - 2
P (drawn 1 newspaper, 1 novella and 2 periodicals) = P (drawn 1 article of each kind) - > d = a - 1

after this you need to use the relation a+b+c+d >= 7 (why?)
replace b, c amd d for the expressions above and find the answer...

2nd
use pascal's triangle and find how many pahts are to reach C, how many to reach D, and get the probability.