contestada

A cupcake stand has 40 chocolate, 30 coconut and 20 banana cupcakes. Alice chooses 20 cupcakes at random to create a box as a present for her friend.
What is the probability that she chose:
(a) Eight banana and 6 coconut cupcakes?
(b) At least 2 chocolate cupcakes?
(c) All cupcakes of the same kind?

Respuesta :

amna04352

Answer:

a) 0.00563

b) 1

c) 0

Step-by-step explanation:

Total = 40+30+20 =90

a) (20C8Ɨ30C6Ɨ40C6)/90C20

= 0.00563

b) 1 - (no chocolate + 1 chocolate)

1 - [(50C20) + (40C1Ɨ50C19)]/90C20

1 - 0.00002478

= 0.9999752187

c) [40C20+20C20+30C20]/90C20

= 0.0000000027045

This is about permutations and combinations.

a) Probability = 0.00563

b) Probability = 0.99997522

c) Probability = 0.0000000027045

  • We are told cupcakes at the stand are;

Chocolate = 40

Coconut = 30

Banana = 20

Total number of chocolates = 40 + 30 + 20

Total number of chocolates = 90

a) Probability that she will choose 8 banana and 6 chocolate cakes if she chooses 20 cupcakes at random will be;

(20Cā‚ˆ Ɨ 30Cā‚† Ɨ 40Cā‚†)/90Cā‚‚ā‚€

(125970 Ɨ 593775 Ɨ 3838380)/50980740277700939310

This gives us Ā  0.00563

b) Probability of at least 2 chocolate cupcakes is;

1 - [P(no chocolate) + P(1 chocolate)]

P(no chocolate) = (50Cā‚‚ā‚€)/90Cā‚‚ā‚€

P(1 chocolate) = (40Cā‚ Ɨ 50Cā‚ā‚‰)/90Cā‚‚ā‚€

Thus;

1 - [P(no chocolate) + P(1 chocolate)] = 1 - [(40Cā‚ Ɨ 50Cā‚ā‚‰) + 50Cā‚‚ā‚€]/90Cā‚‚ā‚€

This gives us; Ā 0.99997522

c) Probability of getting all cupcakes of same kind is;

(40Cā‚‚ā‚€ + 20Cā‚‚ā‚€ + 30Cā‚‚ā‚€)/90Cā‚‚ā‚€

ā‡’ 0.0000000027045

Read more at; https://brainly.com/question/23885729

Otras preguntas