Question

Three rotten apples are mixed with seven fresh apples find the probability distribution of the number of rotten apples , if three apples are drawn one by one with replacement .find the mean of the number of rotten apples .

Answer 1

Answer:

according to the theory of ethylene which makes the rotten apple it makes another Apple to rot so the probability off of rotten apple is 1/1=1 because all the apples are the formula of ethylene rotten.

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Answer 2

Three rotten apples are mixed with seven fresh apples, if three apples are drawn one by one with replacement then, the mean of the number of rotten apples is given as follows.

Here, we need to solve 3 cases, as there are 3 rotten apples.

P(X) = 0, 1, 2, 3

P(0) = no rotten apple is drawn

P(0) = $\dfrac{^7C_3}{^{10}C_3} = \dfrac{7 * 6*5}{10*9*8} = \dfrac{7}{24}$

P(1) = one rotten apple and two fresh apples are drawn

P(1) = $\dfrac{^3C_1 * ^7C_2}{^{10}C_3} = \dfrac{3 * 3*7}{5*3*8} = \dfrac{21}{40}$

P(2) = two rotten apples and one fresh apple are drawn

P(2) = $\dfrac{^3C_2 * ^7C_1}{^{10}C_3} = \dfrac{3*7}{5*3*8} = \dfrac{7}{40}$

P(3) = three rotten apples are drawn

P(3) = $\dfrac{^3C_3 }{^{10}C_3} = \dfrac{1}{120}$

The mean of the distribution,

$\mu = \sum _{x=0}^3 X \times P(X)$

$\mu = 0 \times \dfrac{7}{24}+ 1 \times \dfrac{21}{40}+ 2 \times \dfrac{7}{40}+ 3 \times \dfrac{1}{120}$

$\mu = \dfrac{36}{40} = \dfrac{9}{10}$

Therefore, the mean of the number of rotten apples = 9/10 = 0.9