dawadorjehyolmo19
Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.


22. A husband and a wife apprear in an interview for two vacancies for the same post.The probability of husband's selection is 3÷5 and that of wife's selection is 1÷5. Find the probability that:
(i) both are selected
2) exactly one is selected
3) none is selected​

Sagot :

MrRoyal

Answer:

[tex]P(Both) = \frac{3}{25}[/tex]

[tex]P(One) = \frac{12}{25}[/tex]

[tex]P(None) = \frac{22}{25}[/tex]

Step-by-step explanation:

Given

[tex]P(H) = \frac{3}{5}[/tex]

[tex]P(W) = \frac{1}{5}[/tex]

Solving (a): Both selected

[tex]P(Both) = P(H) * P(W)[/tex]

[tex]P(Both) = \frac{3}{5} * \frac{1}{5}[/tex]

[tex]P(Both) = \frac{3}{25}[/tex]

Solving (b): One selected.

This event can be represented as: HW' or H'W

So:

[tex]P(One) = P(H) * P(W') + P(H') * P(W)[/tex]

Where:

P(W') = 1 - P(W) and P(H') = 1 - P(H).

So:

[tex]P(One) = \frac{3}{5} * \frac{4}{5} + \frac{2}{5} * \frac{1}{5}[/tex]

[tex]P(One) = \frac{12}{25} + \frac{2}{25}[/tex]

[tex]P(One) = \frac{12}{25}[/tex]

Solving (c): None selected.

This is the complement of (a) above.

i.e.

[tex]P(None) = 1 - P(Both)[/tex]

[tex]P(None) = 1 - \frac{3}{25}[/tex]

[tex]P(None) = \frac{25 - 3}{25}[/tex]

[tex]P(None) = \frac{22}{25}[/tex]

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.