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# Generalizing k scores in n attempts

Sal generalizes 2 scores in 6 attempts to k scores in n attempts.

## Want to join the conversation?

• Could someone please (1-f)^n-k more? I just kind of get n-k but not 100%. • What if you wanted to know what was the probability of making AT LEAST 2 free throws? How would the formula change? • You just have to sum the relevant probabilities.

In this case it would be easiest to add up the probabilities of getting 0 and 1 free throw, which gives you the probability of NOT making AT LEAST 2 free throws (i.e. making less than 2 free throws). You would then subtract that from 1 to get the probability of making AT LEAST 2 free throws.
`P(AT LEAST 2 free throws) = 1 - P(less than 2 free throws) P(less than 2 free throws) = P(0 free throws) + P(1 free throw) = 6C0 • 0.7⁰ • 0.3⁶ + 6C1 • 0.7¹ • 0.3⁵ = 1 • 1 • 0.000729 + 6 • 0.7 * 0.00243 = 0.000729 + 0.010206 = 0.010935P( AT LEAST 2 free throws) = 1 - 0.010935 = 0.989065 `

Note: 6C0 and 6C1 mean '6 choose 0' and '6 choose 1'.
• Hi All

I tried to calculate the probability for getting 10 Heads out of tossing the fair coin 20 times using the formula for Binomial Distribution and the answer I got is 17.6 % apprx. But why does it appear at first glance that I have a 50% chance of getting Heads for 10 times out of 20 coins tosses.? Am I missing something here? what mistake am I doing? • You're taking the (correct) assumption that a fair coin will land on heads 50% of the time, and extrapolating (falsely) that it means that is must land on heads 10 out of 20 times.

Take your incorrect extrapolation and run it against an odd number of trials to better see your logic mistake. A coin flipped 3 times will not land on heads 1.5 times, since that is impossible.

That it lands on heads 10 (half) of the time is the most likely event. Assuming your math was correct, at 18%. The next most likely event would be that it lands on heads 9 or 11 times. The next most likely event 8 or 12 times.... 7 or 13 times... the least likely event it lands on heads 0 or 20 times... but it's still POSSIBLE that it lands on heads 20 times. That's another way to see why 50% was likely incorrect... there's just too many possibilities for one of them to command 50%
• I really miss the fast/slow play feature of the videos
could you bring that back • fk is success and (1-f) is failure right? • Hi, Mauro here. In the event n=k, we have (n-k)!=0 in the denominator. How do we get rid of these guys? If I flip a coin twice and want to know P(exactly 2 heads),I get 2C2*0.50^2*0.50^0. Empirically, I know it's going to be 0.25, in which case 2C2=1. But why? I hate mindless memorization. Thanks. • What makes this different from the Combinatorics & Probabilities video? Or are they the same? I'm just confused because I feel like I watched similar examples in the combinatorics & probabilities video when calc free throws. • How will the above method differ if the question was probability of making at least 2 scores in a row? • Why use `K` and `N` ? and could you use this with anything in life?  