probability achiever 1

[xtra333]

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what is the probability of getting three heads and two tails in fie consecutive tosses of the same coin?

I understand why 5C3 equals 10. And then the achiever explains the total number of events as 2^5=32. I do not understand why the total sample space is 32.

Also, why is the two tails not counted? is it because 2C2=1 ?

 

[xtra333]

this question comes from achiever exam 1. for DAT

 

[Ferferi]

Probability of getting three heads : 1/2^3
Probability of getting two tails: 1/2^2
1/8 *1/4 =1/32

 

[xtra333]

but achiever says the answer is 10/32

 

[xtra333]

bump... can someone clarify how to do this problem?

 

[oms47]

5C3=5C2

so the heads and tails is accounted for. I just don't get which one you take into account.

 

[oms47]

also 5C3 is there to determine the total possible combinations to get three heads and two tails. but how many total H/T combinations can you get when you toss a coin 5 consecutive times. 2 options for first flip, 2 options for second flip....2 options for fifth flip. 2*2*2*2*2=32

32 total options...of which only 10 possible ways to get 3 heads and two tails

therefore 10/32 or 5/16