Question

suppose a cookie jar had 20 cookies.

• 10 chocolate chip cookies (c)
• 7 snickerdoodles (s)
• 3 peanut butter cookies (p)

write all answers as fractions. do not simplify.
suppose you randomly take 1 cookie.
a) what is the probability that you randomly took a chocolate chip cookie?
p(c) = _________
b) what is the probability that you randomly took a snickerdoodle or a chocolate chip cookie?
p(s or c) = _________
suppose you take 2 cookies randomly.
c) what is the probability that both cookies are a snickerdoodles?
p(s and s) = _________
d) what is the probability that the first cookie is chocolate chip and the second cookie is peanut butter?
p(c and p) = _________
blank 1:
blank 2:
blank 3:
blank 4:

Explanation:

Step1: Probability formula

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Part a

For the probability of taking a chocolate - chip cookie ($P(C)$), the number of favorable outcomes (chocolate - chip cookies) is $n(C) = 10$, and the total number of outcomes (total cookies) is $n(T)=20$. So, $P(C)=\frac{10}{20}$.

Step3: Part b

For the probability of taking a snickerdoodle or a chocolate - chip cookie ($P(S\ or\ C)$), we use the formula $P(A\cup B)=P(A)+P(B)$ (since the events of taking a snickerdoodle and a chocolate - chip cookie are mutually exclusive). Here, $n(S) = 7$ and $n(C)=10$, $n(T) = 20$. So, $P(S\ or\ C)=\frac{7 + 10}{20}$.

Step4: Part c

For the probability of taking two snickerdoodles ($P(S\ and\ S)$), for the first draw, the probability of taking a snickerdoodle is $P_1(S)=\frac{7}{20}$. After taking one snickerdoodle, there are $n = 19$ cookies left and $6$ snickerdoodles left. So, for the second draw, $P_2(S)=\frac{6}{19}$. Using the multiplication rule for independent (in the sense of sequential non - replacement) events $P(S\ and\ S)=P_1(S)\times P_2(S)=\frac{7}{20}\times\frac{6}{19}$.

Step5: Part d

For the probability of taking a chocolate - chip cookie first and then a peanut - butter cookie ($P(C\ and\ P)$), for the first draw, $P_1(C)=\frac{10}{20}$. After taking a chocolate - chip cookie, there are $n = 19$ cookies left and $3$ peanut - butter cookies left. So, for the second draw, $P_2(P)=\frac{3}{19}$. Using the multiplication rule for sequential non - replacement events $P(C\ and\ P)=P_1(C)\times P_2(P)=\frac{10}{20}\times\frac{3}{19}$.

Answer:

a) $\frac{10}{20}$
b) $\frac{10 + 7}{20}$
c) $\frac{7}{20}\times\frac{6}{19}$
d) $\frac{10}{20}\times\frac{3}{19}$