You are running an experiemnt in which you will be administering a physiological

Question

You are running an experiemnt in which you will be administering a physiological test to lizards and looking for differences between males and females. You can only test one animal per day, and you will collect 6 total experiemntal animals from the field, 3 males and 3 females, and trial on 6 consecuative days.

You plan to randomly pick the order in whichyou test the naimals, but then a question comes up: maybe the ammount of time lizards spend in captivity before their turn to be trialed arrives will affect performance. If you get all females first or all males first by chance, then it might be hard to tell if there are any effects of sex or if this is just the influence of what order they were trialed in.

If you assign each lizard a day randomly, what is the probability you will end up with either all males or all females scheules for the first 3 of your 6 trials? ex. MMMFFF

Explanation / Answer

Probability that i will end up with either males or females)

Pr(initial three catches are of same gender) = Pr(all 3 initial catch are males) + Pr(all three initial catches are females)

Pr(all 3 initial catches are males) = Pr(First catch is male) * Pr(second catch is male) * Pr(third catch is male)

= 3/6 * 2/5 * 1/4 = 1/20

Pr(all 3 initial catches are femaales) = 3/6 * 2/5 * 1/4 = 1/20

Pr(all 3 initial catches are on same gender) = 1/20 + 1/20 = 1/10 = 0.1

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