Consider a cupcake shop that sells 7 different kinds of cupcakes (chocolate raspberry, strawberry shortcake, red velvet, funfetti, lemon, German chocolate, and chocolate caramel). Assuming there are at least 12 of each kind available, if Andres asks for a random selection of 12 cupcakes, what is the probability that he will get (a)exactly 6 red velvet?
(b)exactly 3 each of 4 different kinds?
(c)no lemon?
(d)at least 1 German chocolate and at least one chocolate raspberry?

If Andres asks for a random selection of 12 cupcakes, the Probability of choosing:

a)exactly 6 red velvet?

The probability that 6 will be red velvet = 6/12 x 14.3% = 7.2%

(b)exactly 3 each of 4 different kinds?

Since 3 x 4 = 12

The probability that the 12 will be 3 each from 4 different kinds

= 14.3%

(c)no lemon?

Probability of getting a lemon cupcake = 1/7 = 14.3%

Therefore, probability of not getting a lemon cupcake = 100% - 14.3% = 85.7%

(d)at least 1 German chocolate and at least one chocolate raspberry?

The probability of at least 2 being 1 German and 1 chocolate raspberry

= 2/12

= 16.67%

Step-by-step explanation:

a) Probability of each kind of Cupcake

Kind of Cupcakes         Quantity  Probability

chocolate raspberry      12            14.285%

strawberry shortcake    12            14.3%    

red velvet                       12            14.3%

funfetti                            12            14.3%

lemon                             12            14.3%

German chocolate         12            14.3%

chocolate caramel         12            14.3%

b) The probability of choosing a kind of cupcake is the chance that, for example, a strawberry cupcake is chosen instead of the other six kinds.  It expresses the opportunity that an event has in happening out of many other events that could have happened.