Calculating Probability of Getting 3 Heads in a Row in 64 Tosses

In summary, the conversation is about finding the probability of getting 3 heads in a row out of 64 tosses. The person is currently in exam block and can only think about the physics they are studying, specifically using nCr and nPr. The conversation also discusses the probability of getting heads in one, two, three, and four tosses, as well as the total number of possibilities and how to find the sample space.
  • #1
Yura
39
0
my brother needs to know this but I'm in exam block right now and can only think of the physics I am studying this term. i can't remember how to figure this out anymore i just know i'll have to use nCr and nPr.
heres the question:
how do i find the probability of getting tossing 3 heads in a row out of 64 tosses?

thanks
 
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  • #2
Suppose you had one toss only. What is the prob. of a head?

Suppose two tosses. What is the prob. of 2 heads?

Suppose 3 tosses. What is the prob. of 3 heads?

Now, the hard one: in 4 tosses, what is the prob. of one head only? The prob. of 2 heads (regardless of their order)?

The really difficult ones: with 4 tosses, what is the prob. of 2 heads in a row? 3 heads in a row?
 
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  • #3
1st find the desired sample space ie: how many ways are there to have 3 heads in a row out of 64 tosses? don't rush to nCr and nPr just now, think about the possibilities.
then find the total number of possibilities and use the definition a probability.
 
  • #4
To find the sample space you might start from just one toss, then 2 tosses, then 3, 4, ... etc. and make a list of all possible outcomes for each case.
 

FAQ: Calculating Probability of Getting 3 Heads in a Row in 64 Tosses

What is the definition of probability?

Probability is a measure of the likelihood or chance that a specific event or outcome will occur. It is often expressed as a number between 0 and 1, with 0 representing impossibility and 1 representing certainty.

What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability, on the other hand, is based on actual observations and data from experiments or real-life events.

How is probability calculated?

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This can be expressed as a fraction, decimal, or percentage.

What is a sample space in probability?

A sample space is the set of all possible outcomes of a particular event or experiment. It can be represented using a list, table, or tree diagram.

Can probability be greater than 1 or less than 0?

No, probability cannot be greater than 1 or less than 0. A probability of 1 represents certainty, while a probability of 0 represents impossibility. Any value outside of this range would not make sense in the context of probability.

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