Suppose that a person chooses a letter at random from RESERVE

[TomJerry]

Suppose that a person chooses a letter at random from "RESERVE"

Question :
Suppose that a person chooses a letter at random from "RESERVE" and then chooses one at random from "VERTICAL" . Find the probability that the same letter is choosen.

Solution:

Probability of choosing letter from "RESERVE" is P(A) = 1/7

Probability of choosing letter from "VERTICAL" is P(B) = 1/8

Probability of choosing letter which exist in both would be P(A intersection B) = P(A) . P(B)

= 1/56 [Is this correct]

 

[tiny-tim]

Hi TomJerry!

Probability of choosing letter from "RESERVE" is P(A) = 1/7

Probability of choosing letter from "VERTICAL" is P(B) = 1/8

Probability of choosing letter which exist in both would be P(A intersection B) = P(A) . P(B)

= 1/56 [Is this correct]

erm … on that basis, the probability of choosing the same letter from "CAT" and "MOUSE" would be 1/15 …

but it's obviously zero! ​

Start again

 

[Datamedic]

I imagine it must be done letter by letter:
For "RESERVE"
p(R)=2/7
p(E)=3/7
p(V)=1/7

To get a match, you will need to hit the matching letter(s) in "VERTICAL".
In this case, each of the three target letters appears once, thus the probability for each of them is 1/8.

So, the odds of selecting the SAME letter in both words:
R = 2/7 * 1/8, or 2/56;
E = 3/7 * 1/8, or 3/56;
V = 1/7 * 1/8, or 1/56;

and the odds of making ANY of them is their sum 6/56, or 3/28...

 

[Fredrik]

Datamedic, that's a good explanation, but the forum policy on homework and textbook-style questions is to give hints, not complete solutions. So keep that in mind next time, and welcome to Physics Forums.

 

[statdad]

The OP seems to be spreading homework questions around in several spots outside the homework section.