0
$\begingroup$

k dice are thrown. Compute the probabilities of the following two events: A - the largest number that occurred is i.

I tried the following solution but it is not equal to the final answer:

I Tried to define the size of A and then divide it by $$ {6^k} $$

|A| = $$ { {k \choose 1} i^{k-1} } $$

(Need to choose place for "i" and than I have i options for each of the other places.

Any thoughts why it is wrong? thank you

  • 1
    You mention "two events"... – 2017-02-15
  • 1
    For the event $A$, Hint: it is significantly easier to compute the probability that the largest element is $≤i$. That's just $\frac {i^k}{6^k}$. – 2017-02-15
  • 1
    Note: your computation is flawed as it multiply counts instances in which $i$ appears multiple times. – 2017-02-15
  • 0
    Thank you , I understand my mistake! – 2017-02-15
  • 0
    Hint: If rv $X$ denotes the largest number that occurs then $\{X=i\}$ and $\{X\leq i-1\}$ are disjoint events with $\{X=i\}\cup\{X\leq i-1\}=\{X\leq i\}$ – 2017-02-15

1 Answers 1

0
  1. $P(n>i)=\left(\frac{6-n}{6}\right)^k$
  2. $P(n
  3. $P(n=i)=1-P(n>i)-P(n