A box contains 10 red marbles and 10 green marbles. Sampling at random from this box five times without replacement, you have drawn a red marble all five times. Without replacing any of the marbles, what is the probability of drawing a red marble the 6th time?

The required probability of drawing a red marble the 6th time is 1/2.

Given that,

A box contains 10 red marbles and 10 green marbles.

Sampling at random from this box five times without replacement, you have drawn a red marble all five times.

Without replacing any of the marbles.

We have to determine,

What is the probability of drawing a red marble the 6th time?

According to the question,

There are 10 red marbles and 10 green marbles,

The initial condition is to the same state at every step, so the probability to get a red marble is the same in each sampling  and is equal to the ratio of the number of red marbles to the total number of samples.

Therefore,

The probability of drawing a red marble the 6th time is,

Hence, The required probability of drawing a red marble the 6th time is 1/2.

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5/15 is the probability of choosing a red marble from the box.

Step-by-step explanation:

We know that,

There are 5 red marbles and 10 green marbles in the box.

Divide the number of events by the number of possible outcomes. This will give us the probability.

P(red marble) = P(5)

Possible outcomes

5 red, 10 green -> 15 possibilities

Probability =

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(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3