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 two red marbles, two green ones, four white ones, and two purple ones. She grabs seven of them. Find the probability of the following event, expressing it as a fraction in lowest terms.

She does not have all the red ones.

Answer 1

# of red marbles = 2

# of green marbles = 2

# of white marbles = 4

# of purple marbles = 2

Suzan grabs 7 marbles at a time.

Then we need to find probability of having no red marbles.

P( no red marble)= # of favourable outcomes/total # of outcomes.

Favourable outcomes:

Put aside 2 red marbles from 10 marbles,then there are 8 marbles.

From these 8 , number of ways 7 marbles can be selected= 8c7 =8c1 = 8

Total number of outcomes:

This is the # of ways that 7 marbles out of total 10 can be selected = 10c7 =10c3 = 120

Hence,

P( no red marble) = 8/120 =1/15 Answer