There are 52 cards in a deck with 13 cards of each of the four suits. Marlin draws one card, put its back and draws another one.What is the probability that she draws a hearts card and then a 6? Enter your answer as a fraction or a decimal rounded to the nearest hundredth.

Solution

T h ere a re 52 c a r d s in a d ec k w i t h 13 c a r d s o f e a c h o f t h e f o u r s u i t s . M a r l in d r a w s o n e c a r d, p u t i t s ba c k an d d r a w s an o t h er o n e . Wha t i s t h e p ro babi l i t y t ha t s h e d r a w s a h e a r t s c a r d an d t h e n a 6 ? E n t er yo u r an s w er a s a f r a c t i o n or a d ec ima l ro u n d e d t o t h e n e a res t h u n d re d t h .

\frac{1}{52}

Decimal

0.01923 \dots

Solution steps

Find the probability of she draws a hearts card:

\frac{1}{4}

Find the probability of then a 6:

\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}{4} \cdot \frac{1}{13}

\frac{1}{4} \cdot \frac{1}{13} = \frac{1}{52}

= \frac{1}{52}