1

Flip 100 coins

  1. define a random variable that counts the number of heads
  2. probability of getting exactly 5 heads
  3. probability of getting at least 1 head
  4. find the expected number of heads using the random variable defined above

So far I know there are $2^{100}$ possible outcomes, but I stuck from there.

Liam B
  • 3
SSS
  • 397

1 Answers1

0

probability of getting n heads = $\dfrac{\binom{100}{n}}{2^{100}}$ since the denominator expresses the number of ways you can get n heads and the denominator is all th epossible cases.

The probability of getting 5 heads then is $\dfrac{\binom{100}{5}}{2^{100}}$.

The probability of getting as least one head is the same as the probability of not getting 0 heads. This is $1-\dfrac{\binom{100}{1}}{2^{100}}=1-\dfrac{1}{2^{100}}$

Now to find the expected value we need to sum up the probability you get n heads multiplied by n. (so its gives you sort of like an average sum of heads after many experiments).

so this is $\sum_{n=0}^{100}\dfrac{\binom{100}{n}}{2^{100}}*n$

Asinomás
  • 105,651