Probability of scoring a penalty

[urbantrained]

The probability that I take a penalty and score is 2/5.

If I take 10 penalties, what is the probability that I score less than 50% of them?

 

[jcsd]

My gut instinct tells me the answer should be:

(10!/4!6!)(3/5)⁶(2/5)⁴ + (10!/3!7!)(3/5)⁷(2/5)³ + (10!/2!8!)(3/5)⁸(2/5)² + (10!/9!)(3/5)⁹ 2/5 + (3/5)¹⁰

but I've not checked it throughly

 

[jcsd]

The above gives an answer of ~0.633 which seems about right to me.

 

[jcsd]

I've just done a quick check and the above is indeed the correct answer.