Question

A cookie jar contains 2 chocolate chip cookies, 5 oatmeal raisin cookies, and 3 sugar cookies.

Event A= drawing A chocolate chip cookie on the first draw

Event B= drawling a sugar cookie on the second draw

If two cookies are drawn from the jar, one after the other and not replaced, what is P(A and B) expressed in simplest form?

A. 1/15

B. 1/5

C. 3/10

D. 1/3

Answer 1

The answer willl be a) 1/15, because in the question, it tells you that the event B happens without replacement. A will be 2/10 because theres two chocolate chip cookies out of all 10 items in the jar and probability of b) will be 3/9 as you have to take one away guven that there is no replacement. You then times the two probabilities together: 2/10 x 3/9 which gives you 6/90. This is then simplified into 1/15 by dividingboth parts of the fraction by a common factor :3. The answer will be A

Answer 2

`|\Omega|=10\cdot9=90\\ |A\cap B|=2\cdo3=6\\\\ P(A \cap B)=(6)/(90)=(1)/(15)\Rightarrow \text{A}`