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3 years ago

11

Each of urns I and II has 5 red balls, 3 white balls, and 2 green balls. Urn III has 1 red ball, 1 white ball, and 8 green balls

. An urn is selected at random and a ball is drawn. If the ball is green, find the probability that urn III was selected. (Enter your probabilities as fractions.)

1 answer:

LekaFEV [45]3 years ago

3 0

Answer:

The probability of selecting the green ball from urn III is ²/₃

Step-by-step explanation:

Given;

total number of balls in urn I = 10

number of green balls in urn I , = 2

total number of balls in urn II = 10

number of green balls in urn II , = 2

total number of balls in urn III = 10

number of green balls in urn II , = 8

$P = \frac{\frac{8}{10} }{\frac{2}{10} + \frac{2}{10}+ \frac{8}{10}}\\\\P = \frac{\frac{8}{10} }{\frac{12}{10} }\\\\P = \frac{8}{10} *\frac{10}{12} \\\\P = \frac{8}{12}\\\\ P = \frac{2}{3}$

Therefore, the probability of selecting the green ball from urn III is ²/₃

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Step-by-step explanation:

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2 years ago

Stu trained for a triathlon for 5 hours yesterday. He ran 5 miles and then biked 80 miles. His biking speed is 15 mph faster tha

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Answer:

Step-by-step explanation:

Given as :

The distance cover while running = $D_1$ = 5 miles

Let The speed for running = $S_1$

The distance cover with bike = $D_2$ = 80 miles

The speed for biking = $S_2$ = 15 mph + $S_1$

Total Time taken = 5 hours

Now Time = $\dfrac{\textrm Distance}{\textrm Speed}$

∴ 5 hour = $\frac{D_1}{S_1}$ + $\frac{D_2}{S_2}$

Or, 5 hour = $\frac{5}{S_1}$ + $\frac{80}{15+S_1}$

Or, 5 hour = $\frac{75 + 5 S_1 + 80 S_1}{S_1(15+S_1)}$

or, 5 × ( $S_1^{2}+15 S_1$ ) = $85 S_1 + 75$

Or, $5 S_1^{2} + 75 S_1$ - $85 S_1 - 75$ = 0

or, $5 S_1^{2} -10 S_1 - 75$ = 0

or, $S_1^{2} -2 S_1 - 15$ = 0

Or, $S_1^{2} -3 S_1 + 5 S_1- 15$ = 0

Or, $S_1 (S_1 - 3) + 5 (S_1 - 3)$ = 0

Or, $(S_1 - 3) ( S_1 + 5 )$ = 0

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3 years ago

Carlos deposited $7,924 into a savings account 30 years ago. The account has an interest rate of 4.6% and the balance is current

exis [7]

Answer:

n = 1, this means the interest compounds ANNUALLY.

Step-by-step explanation:

Carlos deposited $7,924 into a savings account 30 years ago. The account has an interest rate of 4.6% and the balance is currently $30,541.83. How often does the interest compound?

Compound Interest Formula

: A = P(1 + r/n)^nt

A = Amount after time t

P = Principal (Initial Amount Invested)

r = Interest rate

n = Number of times the interest is compounded

t = time in years

A = $30,541.83

r = 4.6% = 0.046

t = 30

P = $7,924

Hence,

$30,541.83 = $7924(1 + 0.046/n)^30n

Divide both sides by 7924

$30,541.93/$7924 = (1 + 0.046/n)^30n

$30,541.93/$7924 = (n + 0.046/n)^30n

3.8543576477 = (n + 0.046/n)^30n

We take the logarithm of both sides

log 3.8543576477 = log (n + 0.046/n)^30n

Solving for n,

n = 1

Therefore, from the calculation above, since n = 1, this means the interest compounds ANNUALLY.

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