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Popular Word Problems >

given a standard 52 card deck you randomly choose pick two cards what is the probability both cards are clubs

Solution

g i v e n a s t an d a r d 52 c a r d d ec k yo u r an d o m l y c h oose p i c k tw o c a r d s w ha t i s t h e p ro babi l i t y b o t h c a r d s a re c l u b s

Solution

\frac{1}{16}

+1

Decimal

0.0625

Solution steps

Probability of a club when a card is dealt:

\frac{1}{4}

For multiple independent trials

P (x) = n C x \cdot p^{x} \cdot (1 - p)^{n - x}

number of trials

n = 2

number of successes

x = 2

probability of success in any one trial

p = \frac{1}{4}

P (2) = 2 C 2 (\frac{1}{4})^{2} (1 - \frac{1}{4})^{2 - 2}

2 C 2 = 1

= 1 \cdot (\frac{1}{4})^{2} (\frac{3}{4})^{0}

1 \cdot (\frac{1}{4})^{2} (\frac{3}{4})^{0} = \frac{1}{16}

= \frac{1}{16}

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