Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, four green ones, five white ones, and one purple one. She grabs seven of them. Find the probability of the following event, expressing it as a fraction in lowest terms. She has at least one green.
so far i have that C(13,7)=1716
so after that what would i have to do to get at least the one green probability.
To find the probability that Suzan has at least one green marble, you can calculate the complement of the event "Suzan has no green marbles."
To find the probability of Suzan having no green marbles, you need to consider the total number of ways she could choose seven marbles from the bag, where none of them are green.
To calculate this, you can count the number of ways to choose seven marbles where only red, white, and purple marbles are selected. The possible combinations can be calculated by selecting seven marbles out of the 3 red, 5 white, and 1 purple marbles.
So the number of ways to choose seven marbles with no green is C(3+5+1, 7) = C(9, 7) = 36.
Therefore, the probability of Suzan having no green marbles is 36/1716.
To find the probability of Suzan having at least one green marble, you calculate the complement of the previous probability by subtracting it from one:
P(at least one green) = 1 - P(no green)
= 1 - (36/1716)
= (1716 - 36)/1716
= 1680/1716
Therefore, the probability that Suzan has at least one green marble is 1680/1716, which can be simplified to 35/36.