What are the odds against getting all heads or all tails in three successive flips of a coin?
I say it is 3:1, is this right?
I don't think so. Lets look at it.
There are 2^3=8 things that can happen when you flip three coins.
Two of those HHH,or TTT is heads or tails.
so in 8 tries, one expects 2 heads/tails.
So in 8 trials, six are not heats or tails.
6:2 is the odds, and geepers, you are exactly right. Go to the head of the class.
some of the worst math I've ever seen
No, the odds against getting all heads or all tails in three successive flips of a fair coin are actually 7:1. Let me explain how to calculate it:
To find the odds against an event, we need to consider the number of unfavorable outcomes (outcomes that do not satisfy the given condition) compared to the number of favorable outcomes (outcomes that do satisfy the given condition).
In this case, we want to determine the number of unfavorable outcomes. To do that, we need to calculate the number of outcomes where we either get all heads or all tails. Since each flip of a coin has two possible outcomes (head or tail), there are 2^3 = 8 total outcomes for three successive coin flips.
Now, let's determine the number of outcomes where we get all heads or all tails. There are two possible ways to achieve this: getting all heads (HHH) or getting all tails (TTT). Therefore, the number of favorable outcomes is 2.
Finally, to calculate the odds against getting all heads or all tails, divide the number of unfavorable outcomes (6) by the number of favorable outcomes (2). So, the odds against getting all heads or all tails in three successive coin flips is 6:2 or simplified, 3:1.
To summarize, the correct odds against getting all heads or all tails in three successive coin flips is 7:1, not 3:1.