Question

Marge correctly guessed whether a fair coin turned up "heads" or "tails" on sic consecutive flips. What is the probability that she will correctly guess the outcome of the next coin toss?

Answer 1

Answer with explanation:

It is given that ,Marge correctly guessed whether a fair coin turned up "heads" or "tails" on sic consecutive flips.

When we flip a coin , there are two possible Outcomes, one is Head and another one is Tail , that is total of 2.

Probability of an event

`=\frac{\text{Total favorable Outcome}}{\text{Total Possible Outcome}}`

Probability of getting head

`=(1)/(2)`

Probability of getting tail

`=(1)/(2)`

⇒There can be two guesses , either it will be true and another one will be false.

So, Possible outcome of correct guess={True, False}=2

--Probability of Incorrect(False) guess

`=(1)/(2)`

--Probability of Correct(True) guess in seventh toss

`=(1)/(2)\\\\=(1)/(2) * 100\\\\=50 \text{Percent}`

⇒Probability that she will correctly guess the outcome of the Seventh coin toss, if previous sixth tosses has correct guess

=T×T×T×T×T×T×T, where T=True guess

= 0.5×0.5×0.5×0.5×0.5×0.5×0.5

=0.0078125

=0.0078 (approx)

Answer 2

The probability of guessing a coin flip outcome is 0.5 (50%) and it is independent of the outcome of the previous flips:
P(guessing the 7th flip, after six consecutive flips) = 0.5


Also, we can use the compound probability, which can be found by simply multiplying the probabilities of each event:
P(guessing 7 in a row) = 0.5 × 0.5 × 0.5 × 0.5 × 0.5 × 0.5 × 0.5
= (0.5)⁷
= 0.0078

Hence, the probability that Marge correctly guesses the 7th flip is still 50%, but in general, the probability of guessing 7 consecutive flips is 0.78%.