it's my first question on this forum.

I just purchased Probability and Statistics - Basic book from amazon to refresh and learn what I've never learned. I like the book it explains the subject well. However, I got a different result on one of the examples.

Example: 2 fair dice are rolled. What is the probability of getting a sum less than 7 or a sum equal to 10?

The books claims that P(A) = 15/36 and P(B) = 1/36. And base on that P(A or B) = 4/9.

I agree on P(A) but I believe that P(B) should be equal to 3/36, including {(4,6), (5,5), (6,4)} rolls. Therefore, my final result is P(A or B) = 3/6.

Am I missing something or the book got it wrong?

  • 1
    $\begingroup$ Two comments. P(A and B)=0, the question asks about P(A or B). In this link they make the same mistake you mention. $\endgroup$ – user10525 Apr 28 '12 at 17:25
  • $\begingroup$ I already corrected the question per gung note. It looks like it's the same book. Thanks for the link. Now I have an online version too. $\endgroup$ – Vadim Apr 28 '12 at 17:35

Without bothering to check P(A), you should know that books like this (to include books on pure math, programming, and statistics, as well as probability) always have typos. That's not a remark intended to disparage the authors or editors, etc. It simply isn't possible to have a book like this without something getting by. There is no question that there is more than one way to roll 2 fair dice and get a 10. I would guess that the real typo was to calculate the probability of getting a 12 rather than a 10, but as stated, you're right here.

One other thing, they presumably also meant p(A or B).

  • $\begingroup$ It is p(A or B). I'll correct my questions. Thanks. $\endgroup$ – Vadim Apr 28 '12 at 17:26

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