Hi, below is a problem under binomial distribution and i have answered the problem. Can someone advise if my solution to A below is correct please. Please help me also to solve probability for question 1B.

A. Find the probability that at least 6 of the cuttings take root.

- Mrs. Logan has taken 8 cuttings from a plant which won her first prize in last year’s country fair. She has set the cuttings in individual pots and hopes they will take a root. On the basis of past experience, she knows there is a 0.7 probability that a given cutting will take root.

Solution:

Formula:P= nCr pr qn-r

Where:

p= 0.7

q =0.3

n = 8

r = {6,7,8}

P(X=6) = 8C6 (0.7)6 (0.3)2

= 28 (0.7)6 (0.3)2

= 28 (0.1176)(0.09)

= 0.2964

P(X=7) = 8C7 (0.7)7 (0.3)1

= 8 (0.7)7 (0.3)1

= 8 (0.0824)(0.3)

= 0.1978

P(X=8) = 8C8 (0.7)8 (0.3)0

= 1 (0.7)8 (0.3)0

= 1 (0.0576)(1)

= 0.0576

Since all events (X=6, X=7, X=8) are mutually exclusive, then

P(X>6) = P(X=6) + P(X=7) + P(X=8)

= 0.2964 + 0.1978 + 0.0576

P(X>6)= 0.5518 or 55%

B.Find the probability that more than 2 of the cuttings will take root.

Thanks in advance.