Practice Probability of Heads Up

puremath

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If Miranda flips a coin twice, what is the probability that both coins will land heads up?


Solution (not my work):
Probability of coin 1 landing heads up is 1/2. Probability of second coin landing heads up is 1/2.

P(both heads up) = (1/2)(1/2) = 1/4.

Question:
What indicates in the problem that 1/2 is multiplied by 1/2? Taking a test, a student might guess that he or she must add 1/2 to itself.
 

MarkFL

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We are asked to find the probability that the coin is heads on the first flip AND the coin is heads on the second flip. The "AND" tells us to multiply.
 
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puremath

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We are asked to find the probability that the coin is heads on the first flip AND the coin is heads on the second flip. The "AND" tells us to multiply.
The answer is 1/4.
 

MarkFL

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Yes.
 

puremath

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We are asked to find the probability that the coin is heads on the first flip AND the coin is heads on the second flip. The "AND" tells us to multiply.
The word AND is not in the problem. This is the way I would type the question:

If Miranda flips a coin twice, what is the probability that the coin lands heads up on the first flip and heads up on the second flip? Now the word problem makes sense to me.
 

MarkFL

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When it says both that means both the first flip AND the second flip are heads.
 

MarkFL

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Actually, It could be worded better, as it first implies she is flipping the same coin twice, then it speaks of both coins. If I were to author such a problem, I might state:

If Miranda flips a coin twice, what is the probability that it lands heads up both times?
 
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puremath

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When it says both that means both the first flip AND the second flip are heads.
When reading this the first time, it is not so clear.
 

puremath

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Actually, It could be worded better, as it first implies she is flipping the same coin twice, then it speaks of both coins. If I were to author such a problem, I might state:

If Miranda flips a coin twice, what is the probability that it lands heads up both times?
It is ok but my wording makes it clear to the reader that this problem involves AND and thus multiplication is the operation. Back to Cohen on Monday.
 

MarkFL

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What is the probability that of the two flips, at least one is heads?
 

puremath

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What is the probability that of the two flips, at least one is heads?
P(at least one heads up) = 1 - P(not one is heads up). At the job now. I have a probability book that I also want to learn with you later on in my self-study trek.
 

MarkFL

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You're on the right track. I will give you time to complete the question.
 

puremath

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You're on the right track. I will give you time to complete the question.
For two flips, there are 4 possibilities, only one of which (getting tails twice) does not have any head. So, the other 3 out of 4 cases would have one or two heads. I say 75% probability. Yes?
 
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MarkFL

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Yes, very good! :)
 

puremath

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Yes, very good! :)
Thanks. I can do word problems and precalculus at the same time. Today is Cohen for most of the day. Tomorrow, word problems only from Queens not the house.