Answer: 2343 / 256

Explanation

I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.

1) Adding the terms:

4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0

= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =

= 2343 / 256

2) Using the formula:

n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0

Here n - 1 = 4 => n = 5

r = 3/4

A = 3

Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =

= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =

= (3 * 781) / (4^5) / (1/4) = 3 * 781 / (4^4) = 2343 / 256

So, no doubt, the answer is 2343 / 256

5 0

3 years ago

ou watch a roulette wheel spin 3 consecutive times and each time the ball lands in a red slot. What is the | probability that th

spayn [35]

Answer:

The probability is $\frac{18}{38}=0.4736$

Step-by-step explanation:

The game of roulette wheel consists in spinning a wheel with 38 slots : 18 red, 18 black and 2 green.

If we suppose that the roulette is a fair roulette, then each slot has an equal chance of capturing the ball and given that the ball lands in a red, black or green slot this event doesn't give us information about the following spin. Meaning that exists independence between each spin of the roulette wheel.

In our exercise, we spin the roulette wheel 3 consecutive times and each time the ball lands in a red slot. This doesn't give us information about the fourth spin (because of the independence).

Given that each slot has an equal chance of capturing the ball we can calculate the probability of the ball landing on a red slot on the next spin as :

$P(Red)=\frac{18}{38}=0.4736$

We divide the favourable cases (18 red slots) by the total cases (38 slots) in order to calculate the probability.

The probability is $\frac{18}{38}=0.4736$

6 0

2 years ago