Probability theory and statistics


Postby Guest » Mon Jun 01, 2020 7:39 am

A large number of English managers are visiting a car plant in Japan. They will be shown around in small groups of 6. Twenty percent of the managers speak Japanese. If the groups are picked at random what is the probability that there are at least 5 Japanese speakers in the group?

Re: Probabliltyy

Postby Guest » Wed Jun 17, 2020 2:53 pm

This is a binomial distribution with p= 0.2= 1/5, q= 0.8= 4/5. "At least 5" in a group of 6 is "either 5 or 6" so the probability is [tex]\begin{pmatrix}6 \\ 5 \end{pmatrix} (0.2)^5(0.8)+ \begin{pmatrix}6 \\ 6 \end{pmatrix} (0.2)^6= 6(0.2)^5(0.8)+ (0.2)^6[/tex].

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