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A fair coin is flipped 5 times.
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01 Mar 2023, 01:03
01 Mar 2023, 01:03
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27% (00:53) correct
72% (01:25) wrong based on 29 sessions
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A fair coin is flipped 5 times.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The probability of getting more heads than tails |
1/2 |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Re: A fair coin is flipped 5 times.
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25 Mar 2023, 09:44
25 Mar 2023, 09:44
Expert Reply
OE
Because heads and tails are equally likely, it follows that the probability of getting more heads than tails should be exactly the same as the probability of getting more tails than heads. The only remaining option is that you might get equally as many heads and tails. However, because the total number of coin flips is an odd number, the latter is impossible. Therefore, the probability of getting more heads than tails must be exactly 1/2. (It is, of course, also possible to compute this probability directly by considering the cases of getting 5, 4, or 3 heads separately. However, this approach would be very time-consuming.) Another way of thinking about it is that, for every set of flips that has more heads than tails, there is a corresponding set of flips, in which every flip gets the opposite result, that has more tails. For instance, the sequence of throws HHHHH is balanced by the sequence TTTTT. The sequence HHHHT is balanced by the sequence TTTTH. Therefore, the two quantities are equal.
Because heads and tails are equally likely, it follows that the probability of getting more heads than tails should be exactly the same as the probability of getting more tails than heads. The only remaining option is that you might get equally as many heads and tails. However, because the total number of coin flips is an odd number, the latter is impossible. Therefore, the probability of getting more heads than tails must be exactly 1/2. (It is, of course, also possible to compute this probability directly by considering the cases of getting 5, 4, or 3 heads separately. However, this approach would be very time-consuming.) Another way of thinking about it is that, for every set of flips that has more heads than tails, there is a corresponding set of flips, in which every flip gets the opposite result, that has more tails. For instance, the sequence of throws HHHHH is balanced by the sequence TTTTT. The sequence HHHHT is balanced by the sequence TTTTH. Therefore, the two quantities are equal.
Re: A fair coin is flipped 5 times.
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08 Dec 2023, 07:39
08 Dec 2023, 07:39
1
The probability of getting more heads than tails, means two case 1) HHHTT 2) HHHHT
1) HHHTT = 1/32 * 5!/(3!*2!) = 10/32
2) HHHHT = 1/32 * 5!/4! = 5/32
total probability = HHHTT + HHHTT = 10/32 +5/32 = 15/32 this will slightly less than 1/2
Carcass please check and guide , i am not getting C .
1) HHHTT = 1/32 * 5!/(3!*2!) = 10/32
2) HHHHT = 1/32 * 5!/4! = 5/32
total probability = HHHTT + HHHTT = 10/32 +5/32 = 15/32 this will slightly less than 1/2
Carcass please check and guide , i am not getting C .
