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Video Transcript
Alright. A coin is flipped seven times. What are the possible outcomes? This is how many possible outcomes there are. The first flip could have heads or tails. Alright. You could have tails or heads on the first flip. You could have tails or heads after the next flip. The next flip tails or heads. It's tails. From here, tails and tails. Towels, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails, And yes, tails heads. That's 1234 flips. There are ways to go. So tails, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails, heads, tails. Alright, so you know where I'm going with this. You can have tails, heads, or a mix in between. How many possible outcomes are there? This is the multiplication property. There are two possibilities. So two turns 6. I don't. 1,224, 1, 3456788. This is the first flip. The fourth flip is going to have 16 outcomes. There are 10, 11, 12, 14, 15, 16 characters. It's going to be 32 by the 5th flip. The 6th flip is going to be 64. The 7th flip. 128. 128 total outcomes. How many possible outcomes is the answer? There are 128 possible outcomes. How many outcomes have more tails than heads? There were 1, 2, 3, 4, 5. Okay. I think about 50 because it's going to be 5050 and 64 are going to have more tails than heads. How many possible outcomes have three heads? If I know the first one has to be had, the second one has to be heads, the third one has to be heads, and the rest of them have to be tails. So tails heads. There are heads. Alex tails, tails, tails evidence. I was training. Alright, tails, heads, stop, tails, tails, heads, heads, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, tails, What combination will this be? Maybe it's backwards, where it's three combination 5. Maybe it should be seven positions. Three objects? Yes. Alright. There are 35 possible outcomes. That's going to be seven combination four, right? The next is 35 as well.
Jordan M. I need to know how to figure out the probability of getting heads a single time after flipping a coin seven times. More
2 Answers By Expert Tutors
if you flip a coin once, there are 2 possibilities, H or T (2^1)
if you flip a coin twice, there are 4 possibilities, HH,HT,TH,TT (2^2=4)
three times, 2^3=8
4 times, 2^4=16
5 times, 2^5=32
6 times, 2^6=64
7 times, 2^7=128 total possibilities; this is the denominator
how many ways can the event occur ? 7 ways
HTTTTTT
THTTTTT
TTHTTTT
TTTHTTT
TTTTHTT
TTTTTHT
TTTTTTH
the probability is 7/128
David W.
tutor
Note: Including the words "single time" and "after" confuse this problem somewhat. With a "fair" coin, the probability of getting heads on a "single" flip at any time is 1/2. However, the probability of getting exactly one heads out of seven flips is different (and the solution is given).
This problem is of the type that can be solved with the aid of the binomial distribution.
Since the probability of getting a head on a single flip is 1/2 as is the probability of getting a tail, the binomial distribution gives the desired probability as
7C1 (1/2)7 = 7 /128.
7C1 is the combinatorial coefficient " seven choose 1". The combinatorial coefficients can be obtained from a graphing calculator such as the TI-84, or from Pascal's triangle.
The formal expression for 7C1 is 7!/[ (7-1)! 1! ]
where the ! denotes factorial.
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