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gtnhenbr [62]
3 years ago
5

A bag contains six red marbles three blue marbles and five green marble the three marbles are drawn out of the bag what is the p

robability to the nearest one hundredth that all three marbles will be drawn red?
Mathematics
1 answer:
tia_tia [17]3 years ago
8 0

Answer:

Step-by-step explanation:

Red = 6

Blue = 3

Green = 5

Total = 14

First marble = 6/14  = 3/7  You now have 5 reds and 13 total

Second Marble = 5 * 13  which brings you down to 4 red and 12 total.

Third Marble = 4/12 = 1/3

Result

P(3 Red) = 3/7 * 5/13 * 1/3     cancel the 3s

P(3 Red) = 1/7 * 5/13

P(3 Red) = 5/91

P(3 Red) = 0.0549 . Rounding to the nearest 1/100 depends on what you have been told about rounding. I would say the answer is 0.05 but your teacher may say something different.

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Determine the sum of the first 9 terms in the geometric series where r= -0.25 and a1= 256.
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\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad  \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=-0.25\\ a_1=256\\ n=9 \end{cases}

\bf S_9=256\left(\cfrac{1-(-0.25)^9}{1-(-0.25)}  \right)\implies S_9=256\left( \cfrac{1+0.25^9}{1+0.25} \right) \\\\\\ S_9=256\left(  \cfrac{52429}{65536}\right)\implies S_9=\cfrac{52429}{256}\implies S_9=204.80078125

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