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Popular Word Problems >

Consider a deck of cards. If you draw a single card, what is the probability that you draw a red ace

Solution

C o n s i d er a d ec k o f c a r d s . I f yo u d r a w a s in g l e c a r d, w ha t i s t h e p ro babi l i t y t ha t yo u d r a w a re d a ce

Solution

\frac{1}{26}

+1

Decimal

0.03846 \dots

Solution steps

Find the probability of getting red:

\frac{1}{2}

Find the probability of getting ace:

\frac{1}{13}

Since the events are independent, Use the formula

P (X_{1} \land X_{2} \land \dots \land X_{k}) = P (X_{1}) \cdot P (X_{2}) \cdot \dots \cdot P (X_{k})

= \frac{1}{2} \cdot \frac{1}{13}

\frac{1}{2} \cdot \frac{1}{13} = \frac{1}{26}

= \frac{1}{26}

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