Abox contains 6 red and 8 green marbles. you reach in and remove 3 marbles all at once.
(a) find the probability that these 3 marbles are all red. (enter your answer as a fraction.)
(b) find the probability that these 3 marbles are all of the same color. (enter your answer as a fraction.)

Step-by-step explanation:

(a)Probability that these three marbles are all red

choosing 3 red out of 6 is given by

and choosing 3 marble from 14 marbles=

(b)All of same color

It is possible when they are of either red or green

For red it is

For Green it is

total=

=

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for