Hello math forum.
I have a question.
What are the odds of a number between 1 and 152 being selected 6 Times in 15 chances?
The reason we ask you to show some work is to get some idea what the difficulty you have. Your question can be read at least two ways.
1) Given a number from 1 to 152, what is the probability that number would be randomly and independently selected exactly six times in 15 chances?
OR
2) A number is selected from 1 to 152, what is the probability that same number would be randomly and independently selected exactly 5 more times in 14 chances?
The answers are similar but not the same.
1) $\displaystyle \dbinom{15}{6}\left(\dfrac{1}{152}\right)^{6}\left (\dfrac{151}{152}\right)^{9} $
2) $\displaystyle \dbinom{14}{5}\left(\dfrac{1}{152}\right)^{5}\left (\dfrac{151}{152}\right)^{9} $
I appreciate the help with the formula for your number one. That is the answer I want but I can't do the math on my calculator. I don't know how to do the power of 6 or 9 parts. I would really appreciate the answer being posted or how to do this problem on a scientific calculator. Thanks for any help
I got two of the three numbers I need however, I do not know how to read or factor in the number answer for 1/152 to the sixth power. My calculator shows it as this
8.1084617495525e-14
What do I do with this number? I can't multiply that by the other two numbers in the equation which are
15/6 = 2.5
151/152 to the ninth power = .942323960625871
How do I compute these three numbers using scientific calculator??