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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]

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