# Thread: Discrete Binomial Probability Distributions Questions

1. ## Discrete Binomial Probability Distributions Questions

Hi everyone,

I can't seem to get the answers to these questions.

a) Four marbles are in a jar, with the values 0, 1, 10 and 100 printed on them. Push-up Pete will draw a marble each morning and do that many push-ups. What is the probability that he will draw the “100” marble exactly 2 times in a week

b) Four marbles are in a jar, with the values 0, 1, 10 and 100 printed on them. Push-up Pete will draw a marble each morning and do that many push-ups. What is the probability that he won’t have to do push-ups for exactly one week (7 days in a row)

For a) I tried

P(2)=4Cnr2*(1/4)^2*(3/4)^2
=27/128

but this doesn't seem to work.

Thanks!

2. ## Re: Discrete Binomial Probability Distributions Questions

$p=P[100] = \dfrac 1 4$

$n=7$

$P[\text{2 100s in a week}]= \dbinom{7}{2} \left(\dfrac 1 4\right)^2~\left(1-\dfrac 1 4\right)^{7-2} =$

$21\cdot \dfrac{1}{16}\dfrac{243}{1024} =\dfrac{5103}{16384}$

$P[\text{no pushups in 7 days}] = P[\text{draw 0 7 days consecutively}] = \left(\dfrac 1 4 \right)^7 = \dfrac{1}{16384}$

3. ## Re: Discrete Binomial Probability Distributions Questions

Originally Posted by jugglingbubbles
Four marbles are in a jar, with the values 0, 1, 10 and 100 printed on them. Push-up Pete will draw a marble each morning and do that many push-ups. What is the probability that he will draw the “100” marble exactly 2 times in a week
Here is another question. What is the probability that Pete will do exactly $141$ push-ups in one week?

4. ## Re: Discrete Binomial Probability Distributions Questions

And what is the probability that Pete will survive the week!