Binomial Coefficient

([N],[k])

in Python\ The above cell imports scipy. special, which is a subpackage of scipy and contains method

comb(N,k)

, This method can be used to compute\ binomial coefficient

([N],[k])=(N*(N-1)cdotscdots*(N-k+1))/(k!)=(N!)/(k!(N-k)!)

, i.e. the number of ways of choosing a subset of

k

objects from a set of

N

objects.\ For example, if you need number of ways of choosing 3 out of 7 balls from a box, that number can be found by calling\ scipy.special.

comb(7,3)

\ Feel free to use scipy.special. comb( ) in this assignment.\ In addition, if you want to compute factorial

n!=n*(n-1)*(n-2)*dots*2*1

, you can use\ scipy.special. factorial(

n

)\ Question 1\ A die is rolled 10 times. Let

x

be the number of times six appears in these 10 rolls.\ Part a)\ What is the probability that

xin{4,5}

, i.e. that six appears 4 or 5 times? Do NOT round your answer.\ Write your answer as\ ans

=

some expression>\ For example, if you think the answer is

(1)/(36)

you should create variable ans as\

ans =(1)/(36)

\ IMPORTANT: Just typing 1/36, or answer

=(1)/(36)

is not acceptable. Also, do NOT put dot at the end (this is a python code, not a sentence in\ English). Your answer will be graded automatically, and the test code expects you to create a Python variable called ans, and the code will test the value\ of ans.\ In

[1]:

\ # your code here\ raise NotImplementedError\ In [2]: """'Check whether the answer is numeric and from the interval [0,1] - since it's a probability"""\ assert isinstance(ans, float)\ assert ans

Binomial Coefficient (Nk) in Python The above cell imports scipy. special, which is a subpackage of scipy and contains method comb(N,k), This method can be used to compute binomial coefficient (Nk)=k!N(N1)(Nk+1)=k!(Nk)!N!, i.e. the number of ways of choosing a subset of k objects from a set of N objects. For example, if you need number of ways of choosing 3 out of 7 balls from a box, that number can be found by calling scipy.special. comb(7,3) Feel free to use scipy.special. comb() in this assignment. In addition, if you want to compute factorial n!=n(n1)(n2)21, you can use scipy.special. factorial( n ) Question 1 A die is rolled 10 times. Let X be the number of times six appears in these 10 rolls. Part a) What is the probability that X{4,5}, i.e. that six appears 4 or 5 times? Do NOT round your answer. Write your answer as ans = For example, if you think the answer is 1/36 you should create variable ans as ans=1/36 IMPORTANT: Just typing 1/36, or answer =1/36 is not acceptable. Also, do NOT put dot at the end (this is a python code, not a sentence in English). Your answer will be graded automatically, and the test code expects you to create a Python variable called ans , and the code will test the value of ans. \# your code here raise NotImplementedError """ Check whether the answer is numeric and from the interval [0,1] - since it's a probability""'" assert isinstance(ans, float) assert (0