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Determine whether each of the following is a probability distribution. Give reasons for your answer. - Mathematics and Statistics

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प्रश्न

Determine whether each of the following is a probability distribution. Give reasons for your answer.

x 0 1 2
P(x) 0.3 0.4 0.2
बेरीज

उत्तर

Here, pi > 0, `AA` i = 1, 2, 3
Now consider,
\[\sum\limits_{i=1}^{3} \text{P}_i\] = 0.3 + 0.4 + 0.2 = 0.9 ≠ 1
∴ Given distribution is not a probability distribution.

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पाठ 8: Probability Distributions - Exercise 8.1 [पृष्ठ १४१]

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बालभारती Mathematics and Statistics 2 (Commerce) [English] 12 Standard HSC Maharashtra State Board
पाठ 8 Probability Distributions
Exercise 8.1 | Q 3.(vi) | पृष्ठ १४१

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The probability that a bomb will hit the target is 0.8. Complete the following activity to find, the probability that, out of 5 bombs exactly 2 will miss the target.

Solution: Here, n = 5, X =number of bombs that hit the target

p = probability that bomb will hit the target = `square`

∴ q = 1 - p = `square`

Here, `X∼B(5,4/5)`

∴ P(X = x) = `""^"n""C"_x"P"^x"q"^("n" - x) = square`

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Solution:

Here, n = 4

p = probability of defective device = 10% = `10/100 = square`

∴ q = 1 - p = 1 - 0.1 = `square`

X ∼ B(4, 0.1)

 `P(X=x)=""^n"C"_x p^x q^(n-x)= ""^4"C"_x (0.1)^x (0.9)^(4 - x)`

P[At most one defective device] = P[X ≤ 1]

= P[X=0] + P[X=1]

= `square+square`

∴ P[X ≤ 1] = `square`


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