What is the probability of drawing a 3 or a 4 or a heart from a deck of cards?

1 answer:

5 0

$\Omega=\{2\spadesuit;\ 3\spadesuit;...;A\spadesuit;2\heartsuit ;\ 3\heartsuit;...;A\heartsuit;\ 2\diamondsuit;\ 3\diamondsuit;...;A\diamondsuit;\ 2\clubsuit;\ 3\clubsuit;...;A\clubsuit\}\\\\|\Omega|=52\\\\A=\{3\spadesuit;\ 4\spadesuit;\ 3\diamondsuit;\ 4\diamondsuit;\ 3\clubsuit;\ 4\clubsuit;\ 2\heartsuit;\ 3\heartsuit;\ 4\heartsuit;...;A\heartsuit\}\\\\|A|=2+2+2+13=19\\\\P(A)=\dfrac{|A|}{|\Omega|}\to P(A)=\dfrac{19}{52}$

$Answer:\ \dfrac{19}{52}$

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((Use the graph shown below to fill in the blank.))

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The point (4,y) has a known x coordinate of x = 4. The y coordinate is unknown right now so we'll just call it y.

Draw a vertical line (see side note below) through 4 on the x axis. I've done so in red (see attached image). The red line crosses the graph at the point (4,1) so this tells us that y = 1

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Side Note: you don't have to draw a vertical red line but it's handy to see how it works out. After you get used to these types of problems, you can visually be able to see the answer without these extra lines.