Posted May 6, 2014 2 items from a group of 4 can be selected in 10 distinct ways if repetitions are allowed. e.g. {(1,1),(1,2),(1,3),(1,4),(2,2),(2,3),(2,4),(3,3),(3,4),(4,4)} Are each of these selections equally likely? Why or why not? 0 Share this post Link to post Share on other sites

0 Posted May 6, 2014 no. There are 'technically' 16 possible outcomes some are just equivalent. 1,1 2,2 3,3 4,4 all have a 1/16 chance of occuring while the rest have a 1/8 chance. 1,1 2,2 3,3 4,4 1,2 2,1 2,3 3,2 3,4 4,3 1,3 3,1 2,4 4,2 1,4 4,1 0 Share this post Link to post Share on other sites

0 Posted May 8, 2014 The question is [i think purposely] misleading This is the combinations vs permutations questions with a little slight of hand. If we restate the conditions, I think it would be helpful. The problem says "if repetitions are allowed". So the process must be something like. Reach into a jar and select 1 of 4 marbles [numbered 1 thru 4] record the number of the first marble selected return the marble to the jar Reach into a jar and select 1 of 4 marbles [numbered 1 thru 4] record the number of the first marble selected If this is fair. the distribution for each selection will be [.25, .25, .25, .25] When the results of the second draw are included there will be 16 possible outcomes [permutations] and each will have a probability of 1/16. From a permutations perspective outcomes (12) and (21) are different and each has a likelihood of 1/16. From a combinations perspective outcomes (12) and (21) are the same and this combination has a likelihood of 1/8 The question does not specifically state which is being looked for. BUT since it does not list (12) and (21) as outcomes, this implies that combinations is what is being asked for. For combinations: NO, the outcomes are not equally likely {(1,1),(2,2),(3,3),(4,4)} (4 elements) each occur with P = 1/16 {(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)} (6 elements) each occur with P = 1/8 For permutations: YES. the outcomes are equally likely {(1,1),(1,2),(1,3),(1,4),(style="color: rgb(255, 0, 0);">2,1),(2,2),(2,3),(2,4),(3,1), (3,2),(3,3),(3,4),(4,1),(style="color: rgb(255, 0, 0);">4,2),(style="color: rgb(255, 0, 0);">4,3)(4,4)} (16 elements) each have P=1/16 0 Share this post Link to post Share on other sites

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2 items from a group of 4 can be selected in 10 distinct ways if repetitions are allowed. e.g. {(1,1),(1,2),(1,3),(1,4),(2,2),(2,3),(2,4),(3,3),(3,4),(4,4)}

Are each of these selections equally likely?

Why or why not?

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