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Popular Word Problems >

Example: A card is drawn at random from a standard deck of 52 cards What is the probability of drawing an ace, a 10, or a King?"

Solution

E x am pl e : A c a r d i s d r a w n a t r an d o m f ro m a s t an d a r d d ec k o f 52 c a r d s Wha t i s t h e p ro babi l i t y o f d r a w in g an a ce, a 10, or a K in g ? "

Solution

\frac{3}{13}

+1

Decimal

0.23076 \dots

Solution steps

Find the probability of drawing an ace:

\frac{1}{13}

Find the probability of a 10:

\frac{1}{13}

Find the probability of a king:

\frac{1}{13}

Since the events are disjoint, Use the formula

P (X_{1} \lor X_{2} \lor \dots \lor X_{k}) = P (X_{1}) + P (X_{2}) + \dots + P (X_{k})

= \frac{1}{13} + \frac{1}{13} + \frac{1}{13}

\frac{1}{13} + \frac{1}{13} + \frac{1}{13} = \frac{3}{13}

= \frac{3}{13}

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