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]
