For this problem, assume the balls in the box
are numbered 1 through 6, and that an experiment consists of randomly
selecting 3 balls one after another without replacement.
What probability should be assigned to the event that at least one ball has
an odd number?
I have already found out there are 120 outcomes possible, 1/120 for each outcome. Can you show me how to set this last part up correctly, explaining your steps. Thank you.
are numbered 1 through 6, and that an experiment consists of randomly
selecting 3 balls one after another without replacement.
What probability should be assigned to the event that at least one ball has
an odd number?
I have already found out there are 120 outcomes possible, 1/120 for each outcome. Can you show me how to set this last part up correctly, explaining your steps. Thank you.
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note that selection is without replacement
P[at least 1 odd] = 1 - P[all even] = 1 - 3c3/6c3 = 1 - 1/20 = 19/20 <-------
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another way
P[all 3 even] = 3/6 * 2/5 * 1/4 = 1/20
so P[at least 1 even = 1 - 1/20 = 19/20 <-------
P[at least 1 odd] = 1 - P[all even] = 1 - 3c3/6c3 = 1 - 1/20 = 19/20 <-------
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another way
P[all 3 even] = 3/6 * 2/5 * 1/4 = 1/20
so P[at least 1 even = 1 - 1/20 = 19/20 <-------
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6 x 5 x 4
at first, you choose one from the 6 balls.
and next time. you choose from the rest 5 balls.
at the last, one from 4.
at first, you choose one from the 6 balls.
and next time. you choose from the rest 5 balls.
at the last, one from 4.
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(3/6)(2/5)(1/4) odds all even so 1- this would be at least one odd
1-[(3/6)(2/5)(1/4)]
1-[(3/6)(2/5)(1/4)]