Expert: Josh - 9/12/2006

Question
Hello
Maybe, you will be know how do this exercises.
I have two questions.
Please...

1) "Find the probability of getting a sum of 5 on the first toss of two number cubes and a sum of 6 on the second toss."

2) "A serial number is formed from the digits 1,2 and 3, and the letters A and B. Given that the serial number ends in a letter, what is the probability  that it ends in 2A?"


Thank you for your help...
Pit

Answer
Hello,

For this question, I suggest that you write down various possibilities on paper.

Sum of five can only result from adding 1+4 or 2+3. We note that the order is interchangeable. So, we have 4 combinations out of 6*6 possible outcomes (from tossing two die)......[#a]

For the second toss, a sum of six can only result from adding 1+5, 2+4, 3+3, 4+2, or 5+1. Five combinations will work, out of 6*6 possible outcomes......[#b]

For both events ([#a] and [#b]) to occur, we multiply (4/36) and (5/36) to get the joint probability; assuming that each toss is independent of the previous one.

Q2. Let "VWXYZ" be the serial number.

For, V, W, X and Y, each can take value from the set {"1","2","3","a" and "b"}. For Z, it can take value from {"a","b"} only. Again, each letter in the serial is drawn independently. What this means is we have 5*5*5*5*2 possible outcomes.

Now, impose the restrictions. If Y=2 and Z=a, this event can happen with a probability of (1/5)*(1/2). (Out of five elements, we must choose "2" for Y; and out of two elements, we must choose "a" for Z). There is no restriction for prior letters, V,W and X. So, the prior probability is one.

Ans: 1/10