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Popular Word Problems >

You draw one card from a 52-card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing a two each time.

Solution

Y o u d r a w o n e c a r d f ro m a ​ 52 - c a r d d ec k . T h e n t h e c a r d i s re pl a ce d in t h e d ec k an d t h e d ec k i s ​ s h u ff l e d, an d yo u d r a w a g ain . F in d t h e p ro babi l i t y o f d r a w in g a tw o e a c h t im e .

Solution

\frac{1}{169}

+1

Decimal

0.00591 \dots

Solution steps

The possible outcomes when two cards are drawn are

52 \cdot 52

Therefore, the number of possible outcomes:

5 2^{2}

Find the number of favorable outcomes of drawing a 2 each time:

16

Probability

= \frac{number of favorable outcomes}{total number of outcomes}

= \frac{16}{5 2 ^{2}}

\frac{16}{5 2 ^{2}} = \frac{1}{169}

= \frac{1}{169}

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