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12) A study conducted at a certain college shows that 55% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating

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MrRoyal

Answer:

[tex]P(At\ least\ 1) = 0.9963[/tex]

Step-by-step explanation:

Represent the probability that a graduate finds a job with p

[tex]p = 55\%[/tex]

Required

Determine the probability that at least 1 of 7 gets a job.

In probability:

[tex]P(At\ least\ 1) = 1 - P(None)[/tex]

So, we calculate the probability that none of the 7 gets a job.

Represent the probability that a graduate will not get a job with q.

[tex]q= 1 - p[/tex]

[tex]q= 1 - 55\%[/tex]

[tex]q=45\%[/tex]

Represent as decimal

[tex]q = 0.45[/tex]

The probability that none of the 7 will get a job is [tex]q^7[/tex]

i.e.

[tex]P(None) = q^7[/tex]

So, we have:

[tex]P(At\ least\ 1) = 1 - P(None)[/tex]

[tex]P(At\ least\ 1) = 1 - q^7[/tex]

Substitute 0.45 for q

[tex]P(At\ least\ 1) = 1 - 0.45^7[/tex]

[tex]P(At\ least\ 1) = 1 -0.00373669453[/tex]

[tex]P(At\ least\ 1) = 0.99626330547[/tex]

[tex]P(At\ least\ 1) = 0.9963[/tex] -- approximated

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