Two counters are selected at random from a bag containing 5 red counters and 3 blue counters.

1 answer:

azamat2 years ago

6 0

Answer:

1.4

Step-by-step explanation:

Probability of selecting a red counter :

Number of red counter / total number of counters

5 / (5 + 3) = 5 /8 = 0.625

Probability of selecting a blue counter = 0.375

Let number of red counters :

0, 1 or 2

0 red counters :

Expected value = x * p(x)

0 + (0.625*1) + (0.390625 * 2)

0 + 0.625 + 0.78125 = 1.40625

Expected number of red counters = 1.4

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General Formulas and Concepts:

Algebra I

Calculus

[Area] Limits of Riemann's Sums - Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Step-by-step explanation:

Step 1: Define

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Step 2: Find Area

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[Integral] Rewrite: $\displaystyle \int\limits^2_1 {x^{-4}} \, dx$
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[Area] Fundamental Theorem of Calculus: $\displaystyle \frac{7}{24}$