How to find the designated sum in arithmetic series

. A box in a certain supply room contains four 40-W lightbulbs, five 60-W bulbs, and six 75-W bulbs. Suppose that three bulbs ar

yaroslaw [1]

Answer:

a) 59.34%

b) 44.82%

c) 26.37%

d) 4.19%

Step-by-step explanation:

(a)

There are in total 4+5+6 = 15 bulbs. If we want to select 3 randomly there are K ways of doing this, where K is the combination of 15 elements taken 3 at a time

$K=\binom{15}{3}=\frac{15!}{3!(15-3)!}=\frac{15!}{3!12!}=\frac{15.14.13}{6}=455$

As there are 9 non 75-W bulbs, by the fundamental rule of counting, there are 6*5*9 = 270 ways of selecting 3 bulbs with exactly two 75-W bulbs.

So, the probability of selecting exactly 2 bulbs of 75 W is

$\frac{270}{455}=0.5934=59.34\%$

(b)

The probability of selecting three 40-W bulbs is

$\frac{4*3*2}{455}=0.0527=5.27\%$

The probability of selecting three 60-W bulbs is

$\frac{5*4*3}{455}=0.1318=13.18\%$

The probability of selecting three 75-W bulbs is

$\frac{6*5*4}{455}=0.2637=26.37\%$

Since the events are disjoint, the probability of taking 3 bulbs of the same kind is the sum 0.0527+0.1318+0.2637 = 0.4482 = 44.82%

(c)

There are 6*5*4 ways of selecting one bulb of each type, so the probability of selecting 3 bulbs of each type is

$\frac{6*5*4}{455}=0.2637=26.37\%$

(d)

The probability that it is necessary to examine at least six bulbs until a 75-W bulb is found, supposing there is no replacement, is the same as the probability of taking 5 bulbs one after another without replacement and none of them is 75-W.

As there are 15 bulbs and 9 of them are not 75-W, the probability a non 75-W bulb is $\frac{9}{15}=0.6$

Since there are no replacement, the probability of taking a second non 75-W bulb is now $\frac{8}{14}=0.5714$

Following this procedure 5 times, we find the probabilities

$\frac{9}{15},\frac{8}{14},\frac{7}{13},\frac{6}{12},\frac{5}{11}$

which are

0.6, 0.5714, 0.5384, 0.5, 0.4545

As the events are independent, the probability of choosing 5 non 75-W bulbs is the product

0.6*0.5714*0.5384*0.5*0.4545 = 0.0419 = 4.19%

3 0

3 years ago

HELP ME PLEASE DUE IN 5 MIN

faust18 [17]

Answer:

Step-by-step explanation:

im pretty sur ethe answer is 58... i havent done this is 3 yeras so if its wrong sorry

7 0

3 years ago

What is the line of SYMMETRY for they PARABLLA who’s equation is y=3x2+24x-1?

Arada [10]

Answer

The line of symmetry x = -4

Step by step explanation

Here we have to use the formula.

The symmetry of a parabola x = -b/2a

Now compare the given equation y = 3x^2 + 24x -1 with the general form y = ax^2 + bx + c and identify the value of "a" and "b"

Here a = 3 and b = 24. Now plug in these values in to the formula to find the line of symmetry.

x = -24/ 2(3)

x = -24/6

x = -4

Therefore, the line of symmetry x = -4.

Thank you.

6 0

3 years ago

What is -8 square root of 9 when simplified

gregori [183]

Answer:

$\large\boxed{-8\sqrt9=-24}$

Step-by-step explanation:

$\sqrt{a}=b\iff b^2=a\\\\\sqrt9=3\ \text{because}\ 3^2=9\\\\-8\sqrt9=-8(3)=-24$

7 0

3 years ago

How many ways can Carlos choose 2 pizza toppings from a menu of 4 toppings if each topping can only be chosen once?

Ahat [919]

Answer:

30 different ways

Step-by-step explanation:

Hi

for the first topping she can choose 1 of 6 items

so she has 6 choices

and then the second topping she has 5 choices as each topping can only be chosen once

so it comes 6 * 5 = 30

3 0

3 years ago