In a particular roulette game, there's a 1/36 chance of winning. in a single day, a gambler plays 100 rounds, and wins in 7 of them. what's the p-value for winning 7 or more out of 100 rounds? (hint: be sure you know which kind of probability distribution you're dealing with before you do the calculation.)

0.021739

Step-by-step explanation:

This situation can be modeled with the Binomial Distribution which gives the probability of an event that occurs exactly k times out of n, and is given by

where  

= combination of n elements taken k at a time.

p = probability that the event (“success”) occurs once

q = 1-p

In this case, the event “success” is winning the roulette game with probability 1/36 = 0.027777 and n=100 rounds.

The probability value of winning the roulette game 7 or more times out of 100, is  

P(7;100)+P(8;100)+...+P(100;100) =

1 - P(0;100)+P(1;100)+...+P(6;100)

We can find the sum of these last 7 terms either by hand or computer-assisted and we would find  

P(0;100)+P(1;100)+...+P(6;100) =

and  the p-value (probability value) for winning 7 or more out of 100 rounds is

1-0.978261 = 0.021739

The slope of the line is m=−5138≈−1.34210526315789.

The y-intercept is (0,−14738)≈(0,−3.86842105263158).

The equation of the line in the slope-intercept form is y=−14738−51x38≈−3.86842105263158−1.34210526315789x.

Step-by-step explanation: