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I am solving a problem in probability related to Joint distribution. Let’s say I am playing shooting arrow at a target and after every shot, I choose a number from {2,5}. I shoot twice and everytime I hit the target, I choose 2 and if I do not I choose 5.Let’s suppose the probability of hitting the target is 1/2. So the set of all possible outcomes are {(2,2), (2,5), (5,2), (5,5)}. Let A be the first number chosen so A belongs to {2,5}? Let B be the product of the chosen numbers. Now I am supposed to draw a joint probability distribution table for A and B. And I am not sure if I am doing the correct thing.

My attempt:

So B = {4, 10, 25} and my table looks like this:enter image description here

I am not sure if the corresponding joint probabilities are correct. For example, in order to calculate P(A =2, B =10), my reasoning was. There are four total elements in our sample space. The probability that the first number chosen is 2 AND the product of the two numbers chosen is 10 is only satisfied by (2,5). So, I thought the probability should be 1/4.

Am I doing anything wrong here?

Four Seasons
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  • There are two things unclear. First, are you only allowed to shoot TWICE? Second, for each shooting, what is the probability for hitting the target? But if the answer to the first is affirmative, while for the second the answer is $1/2$, then your solution is correct. – OnoL Feb 02 '18 at 21:14
  • Oh yes. I will edit the question. – Four Seasons Feb 02 '18 at 22:58

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