Question

At a bakery shop, 12 customers bought a vanilla cupcake, 10 chocolate cupcakes, 8 red velvet cupcakes and 7 oranges cupcakes. If a customer is selected at random, identify the probability that she is going to purchase:

I)A red velvet cupcake
II)Vanilla or chocolate cupcake
III)Vanilla or orange or chocolate cupcake
IV)A cupcake that is not orange flavor

Answer 1

Let V be the event that a vanilla cupcake was bought, C be the event that a chocolate cupcake was bought, R be the event that a red velvet cupcake was bought, and O be the event that a orange cupcake was bought.

$$n=12+10+8+7=37$$

$$I)\ P(R)={8 \over 37}$$

$$II)\ P(V\cup C)={12+10\over 37}={22\over 37}$$

$$III)\ P(V\cup O\cup C)={{12+7+10}\over 37}={29\over 37}$$

$$IV)\ P(\bar{O})=1-P(O)=1-{7\over 37}={30\over 37}$$