Question

One morning a customer comes into Pierre’s and orders a random assortment of 6 Danish. At the time she comes in, there are 30 Danish sitting out: 13 apple, 10 cheese, and 7 raspberry. Assume the Danish are not replaced after they are selected. What is the probability that the second, fourth, and fifth Danish selected for the customer’s random assortment will be apple, and the other three will not be apple?

Probability:

What kind of problem is this, where we take things out and don't put them back?:

Answer 1

SOLUTION :

First Danish selected:non- apples

apples; 13 Nos.

Non-apples: 17 Nos.

Total Danish: 30Nos.

So,

P(First Danish selected:non- apples) = 17/30 =0.567

Second Danish selected: apples

apples ; 13 Nos.

Non-apples = 16 Nos.

Total Danish: 29Nos.

So,

P(Second Danish selected: apples) = 13/29 = 0.448

Third Danish selected: Non-apples

apples ; 12 Nos.

Non-apples = 16 Nos.

Total Danish: 28/ Nos.

So,

P(Third Danish selected: Non-apples) = 16/28 = 0.571

Fourth Danish selected: apples

apples ;=12Nos.

Non-apples = 15 Nos.

Total Danish: 27Nos.

So,

P(Fourth Danish selected: apples) = 12/27 = 0.444

Fifth Danish selected: apples

apples; 11Nos.

Non-apples = 15 Nos.

Total Danish: 26 Nos.

So,

P(Fifth Danish selected: apples) = 11/26 = 0.423

Sixth Danish selected: Non-apples

apples ; 10 Nos.

Non-apples= 15 Nos.

Total Danish: 25 Nos.

So,

P(Sixth Danish selected: Non-apples) = 15/25 = 0.6

So,

P(Second , fourth & fifth apples and Others Non apples) = 0.567*0.448*0.571*0.4444*0.423*0.6 = 0.016

So,

Answer is:

0.016.