Agame show airs on television five days a week . each day , a prize is randomly placed behind ome of two doors . the contestant wins the prize by selecting the correct door. what is the probability that exactly two of the five contestants win a prize during a week

There are two possibilities each day (contestant wins or contestant loses).

2^5 = 32 outcomes

But we only want the outcomes where two of the contestants are winners. From the 5 days, pick 2 that will be the winning days.

C(5,2) = (5 * 4) / (2 * 1) = 10 ways

So the probability is 10/32 = 5/16

5/16 = 0.3125 = 31.25%

31.25%

, 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

i would say true? if the unit was informational and it "refreshed your understanding", then true.