Probabilities with fair coin

[Zelda22]

I'm trying to solve this question,

This is what I tried

Probability of at least 4 correct answers out of 5 questions.
A fair coin -2 probability (right or wrong)
Total of probabibities= 2^5 = 32

No of ways to get 4 questions right
5C4= 5!/ 4! (5-4)!= 5

No of ways to get 5 questions right
5C5= 1

At least 4 correct answers
5+1 = 6

So, 6/32 = 3/16

Is this correct?

Thanks

 

[BigBeachBanana]

I'm trying to solve this question,

This is what I tried

Probability of at least 4 correct answers out of 5 questions.
A fair coin -2 probability (right or wrong)
Total of probabibities= 2^5 = 32

No of ways to get 4 questions right
5C4= 5!/ 4! (5-4)!= 5

No of ways to get 5 questions right
5C5= 1

At least 4 correct answers
5+1 = 6

So, 6/32 = 3/16

Is this correct?

Thanks

Looks good.

 

[Dr.Peterson]

There are a couple places where you didn't say what I think you mean:

Probability of at least 4 correct answers out of 5 questions.
A fair coin -2 probability (right or wrong)
Total of probabibities= 2^5 = 32

You probably mean that the probability of being right (or of being wrong) is 1/2, not -2. Or you may mean there are two possibilities.

And you don't mean probabilities, but possible outcomes (the size of the sample space). The total of all probabilities, of course, is 1.

No of ways to get 4 questions right
5C4= 5!/ 4! (5-4)!= 5

No of ways to get 5 questions right
5C5= 1

At least 4 correct answers
5+1 = 6

Here you said it correctly.

So, 6/32 = 3/16

This is the number of successful outcomes over the number of possible outcomes, so it is indeed the probability.

Good work. But be careful how you write!

 

[Zelda22]

Noted. I mean there are two possible outcomes (right or wrong). Thank you.