Question

Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, three green ones, four white ones, and one purple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.] She does not have all the red ones.

Answer 1

SOLUTION :

Total number of marbles is 4+3+4+1 = 12

so , the number of ways to select 8 marbles of 12 = 12!/8!4! == 495.

total number of marbles except green ones is 3+4+1=8

now select all 4 red marbles and remaining 4 marbles from remaining 8 marbles

so,the number of ways to select 4 marbles out of 8 marbles =8!/4!4! =70

so the number of ways to select 8 marbles in which not all red marbles are present 495-70=425.

so,the probability that she does not have all marbles is 425/495 =0.8585