Probability Problem

[schulc76]

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Hey guys, I'm not sure how to figure out this problem, and if someone could explain it that would be awesome!

What is the probability of six tails out of nine tosses of a fair coin?

(Answer is 21/128)


Thanks in advance!!!

 

[riro2]

This is binomial prob.

9 choose 6 * (.5)^6 *(.5)^3

You have a 50% chance of getting tails(success) and a 50% chance of getting heads(failure).

 

[schulc76]

Thanks for trying to help, but I still don't understand. What do you mean by "9 choose 6" ? I understand where you are getting (.5)^6 * (.5) ^3. I don't understand how the full equation comes together or what it looks like.

Thanks.

 

[nainaaz]

Hey guys, I'm not sure how to figure out this problem, and if someone could explain it that would be awesome!

What is the probability of six tails out of nine tosses of a fair coin?

(Answer is 21/128)


Thanks in advance!!!

just remember the formula probability=desired outcomes/possible outcomes

here possible outcomes will be 2^9=512
desired outcomes (order does not matter) which is = 9!/6!*3! = 84
therefore probability = 84/512= 21/128

hope it helps..🙂

 

[riro2]

"Choose" signifies a combination problem. 9 choose 6 simply represents:

(9!)/[ (9-6!)* 6!] .

In variables, this is what we are saying: (n!)/[ (n-r)! * r!]

so when combined in this BINOMIAL prob. you have to multiply this expression by the probability of success and the probability of failure to get the final expression

(9!)/[ (9-6)!* 6!] * (.5)^6 * (.5)^3 = 21/128.

Hope this helps