Question

A sample of four chocolate bars are randomly selected from a box of ten.six of the chocolates in the box are milk chocolate (without replacement). Evaluate Pr(0<p<0.7​

Answer 1

Given:

A sample of four chocolate bars are randomly selected from a box of ten. Six of the chocolates in the box are milk chocolate (without replacement).

To Find:

Evaluate pr (0<p<0.7)?

Solution:

It is given that-

There are total ten chocolate bars in box, out of which 6 are milk chocolate bars.

So, probability of choosing milk chocolate bar is

$p=\dfrac{6}{10}\\\\=0.6$

therefore, probability of not choosing milk chocolate is-

$q=1-0.6\\ =0.4$

Now, choosing 4 chocolate bars from the box , we can choose 0, 1, 2, 3, 4 milk chocolate bars.

Case - 1: when we don't choose any milk chocolate bar.

then, the probability is

$P(\text{Number of milk chocolate bars}=0)=C^{4}_0p^0q^4\\=1\cdot 0.6^0\cdot 0.4^4\\=0.4^4\\=0.0256$

Case - 2: when we choose only one milk chocolate bar.

then, the probability is

$P(\text{Number of milk chocolate bars}=1)=C^{4}_1p^1q^3\\=4\cdot 0.6^1\cdot 0.4^3\\=4\cdot 0.6\cdot 0.064\\=0.1536$

 Case - 3: when we choose only 2 milk chocolate bar.

then, the probability is

$P(\text{Number of milk chocolate bars}=2)=C^{4}_2p^2q^2\\=6\cdot 0.6^2\cdot 0.4^2\\=6\cdot 0.36\cdot 0.16\\=0.3456$

 Case - 4: when we choose only 3 milk chocolate bar.

then, the probability is

$P(\text{Number of milk chocolate bars}=3)=C^{4}_3p^3q^1\\=4\cdot 0.6^3\cdot 0.4^1\\=4\cdot 0.216\cdot 0.4\\=0.3456$

 

Case - 5: when all four choosen chocolates are milk chocolate bar.

then, the probability is

$P(\text{Number of milk chocolate bars}=4)=C^{4}_4p^4q^0\\=1\cdot 0.6^4\cdot 0.4^0\\=1\cdot 0.1296\cdot 1\\=0.1296$