+rep >maths help.

[Teabags]

simple perms and coms.
Find the probability that the first two letters in the order (word NEVER) include exactly one letter E.

Thread moved from 'Discuss Anything' by Matts (Forum Super Moderator)

[hamheyelliot]

Okay, so to find this probability we need to calculate the likelihood of these two:

First is an E, but second is not and
Second is an E, but first is not

The likelihood that the first letter will be an E is 2/5, then the chance the second letter is not an E becomes 3/4 (since there are now 4 letters to choose from and we've found an E already.

So the probability of First is an E, but second is not is:

2/5 x 3/4 = 6/20, cancels down to 3/10

Now we do the same for the next one:

The chance the first is not an E is 3/5, times the probability that the second is an E: 2/4 (because there are now 4 total letters, and still 2 Es to find)

3/5 x 2/4 = 6/20, cancels down to 3/10 again

Now we combine those two probabilities:

3/10 x 3/10 is 6/10, cancels to 3/5

So it's 3/5!

[Teabags]

Okay, so to find this probability we need to calculate the likelihood of these two:

First is an E, but second is not and
Second is an E, but first is not

The likelihood that the first letter will be an E is 2/5, then the chance the second letter is not an E becomes 3/4 (since there are now 4 letters to choose from and we've found an E already.

So the probability of First is an E, but second is not is:

2/5 x 3/4 = 6/20, cancels down to 3/10

Now we do the same for the next one:

The chance the first is not an E is 3/5, times the probability that the second is an E: 2/4 (because there are now 4 total letters, and still 2 Es to find)

3/5 x 2/4 = 6/20, cancels down to 3/10 again

Now we combine those two probabilities:

3/10 x 3/10 is 6/10, cancels to 3/5

So it's 3/5!

oh you wonderful person. Good job I checked - not sure how I got 2/5
Thanks

Now we combine those two probabilities:

3/10 x 3/10 is 6/10, cancels to 3/5

So it's 3/5!

but 3/10 x 3/10 = 9/100
Did still understand it's add not times.

[hamheyelliot]

but 3/10 x 3/10 = 9/100
Did still understand it's add not times.

Oops, yeah - the last one is an addition, not a multiplication - my mistake!