In a box of assorted cookies, $36\%$contain chocolate and $12\%$contain nuts. Of those, $8\%$contain both chocolate and nuts. Sean is allergic to both chocolate and nuts.

a. Find the probability that a cookie contains chocolate or nuts (he can't eat it).

b. Find the probability that a cookie does not contain chocolate or nuts (he can eat it).

In a box of assorted cookies, $36\%$contain and $12\%$contain nuts. Of those, $8\%$contain both chocolate and nuts.

Let us assume the events as follows:

$C=$Event that cookie has chocolates

$N=$Event that cookie has nuts

We have

$$\begin{gathered} P\left(C\right)=0.36 \\ P\left(N\right)=0.12 \\ P\left(CANDN\right)=0.08 \end{gathered}$$

We need to calculate the probability that a cookie contains chocolate or nuts

Thus is given as $P\left(CORN\right)$

$P\left(C\text{OR}N\right)=P\left(C\right)+P\left(N\right)-P\left(CANDN\right)$

Substituting the values, we get

$$\begin{gathered} P(CORN)=0.36+0.12-0.08 \\ P\left(C\text{OR N}\right)=0.50-0.08 \\ P(CORN)=0.42 \end{gathered}$$

In a box of assorted cookies, $36\%$contain and $12\%$contain nuts. Of those, $8\%$contain both chocolate and nuts.

Let us assume the events as follows:

$C=$Event that cookie has chocolate

$N=$Event that cookie has nuts

We have

$$\begin{gathered} P\left(C\right)=0.36 \\ P\left(N\right)=0.12 \\ P\left(CORN\right)=0.42 \end{gathered}$$

We need to calculate the probability that a cookie does not contain chocolate or nuts

Thus is given as $P\left(CORN\right)\text{'}$

$P(CORN{)}^{\text{'}}=1-P(CORN)$

Substituting the values, we get

$$\begin{gathered} P(CORN{)}^{\text{'}}=1-0.42 \\ P(CORN{)}^{\text{'}}=0.58 \end{gathered}$$