Question

Under this hypothesis, what is the probability that eight planets would end up traveling in the same direction? (hint: it's the same probability as that of flipping a coin eight times and getting all heads or all tails.)

Answer 1

The probability that eight planets would end up traveling in the same direction is 1/256.

Step-by-step explanation:

The probability of flipping a coin and getting Heads or Tails is 1/2 for each flip.

To find the probability of flipping a coin eight times and getting all Heads or all Tails, we can use the multiplication rule. Since each flip is independent of the others, the probability of getting all Heads or all Tails is:

(1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/256

Therefore, under the given hypothesis, the probability that eight planets would end up traveling in the same direction is 1/256.

Answer 2

The required probability is 0.0078125.

Step-by-step explanation:

Consider the provided information.

We need to find the probability that eight planets would end up traveling in the same direction.

In our solar system planets can rotates either counter-clockwise or clockwise as seen from above the north pole.

That means we have two possible directions for eight planets, either counter-clockwise or clockwise.

The probability that eight planets would end up traveling in the same direction is same as getting all heads or all tails.

The total number of favorable outcomes are 2, because all the planets either can move counter clockwise or clockwise.

The total number of outcomes are =
`2^(8)`

Hence, the required probability is:

`Probability = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}`

`Probability = (2)/(2^8)=(1)/(2^7)`

`Probability =(1)/(128)=0.0078125`

Hence, the required probability is 0.0078125.