Get the solution to "With n=13 and p=0.4, how do you find..."

Urdorfs4u

Answered question

2022-02-10

With

n = 13

and

p = 0.4

, how do you find P(at least 7) using a binomial probability table?

budniji8d1

Beginner2022-02-11Added 15 answers

Step 1
In a binomial probability distribution, if the probability of success for an event is p (i.e. for failure the probabilty is

(1 - p)

)
the probability of getting r successes out of a total trial of n events i.e.

P (n, r)

is given by

P (n, r) = \frac{n!}{r! (n - r)!} {(1 - p)}^{n - r}

In the given case we have

p = 0.4, n = 13

and at least 7 success means success of 7 or more.
Hence desired probability

P (r \geq 7)

= P (7, 13) + P (8, 13) + P (9, 13) + P (10, 13) + P (11, 13) + P (12, 13) + P (13, 13)

= \frac{13!}{7! 6!} \times {0.4}^{7} \times {0.7}^{6} + \frac{13!}{8! 5!} \times {0.4}^{8} \times {0.7}^{5} + \frac{13!}{9! 4!} \times {0.4}^{9} \times {0.7}^{4} + \frac{13!}{10! 3!}

\times {0.4}^{10} \times {0.7}^{3} + \frac{13!}{11! 2!} \times {0.4}^{11} \times {0.7}^{2} + \frac{13!}{12! 1!} \times {0.4}^{12} \times {0.7}^{1} + \frac{13!}{13! 0!} \times {0.4}^{13} \times {0.7}^{0}

= 0.13117 + 0.06559 + 0.02429 + 0.00648 + 0.00118 + 0.00013 + 0.00001

= 0.22885

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