card is taken out at random from a pack of 52 cards. A second card is selected without replacing the first one. Find the probability that the first card chosen is jack of club and the second card chosen is the king of spades?

Solution

c a r d i s t ak e n o u t a t r an d o m f ro m a p a c k o f 52 c a r d s . A seco n d c a r d i s se l ec t e d w i t h o u t re pl a c in g t h e f i rs t o n e . F in d t h e p ro babi l i t y t ha t t h e f i rs t c a r d c h ose n i s ja c k o f c l u b an d t h e seco n d c a r d c h ose n i s t h e kin g o f s p a d es ?

\frac{1}{2704}

Decimal

0.00036 \dots

Solution steps

Find the probability of getting jack:

\frac{1}{13}

Find the probability of getting club:

\frac{1}{4}

Find the probability of getting king:

\frac{1}{13}

Find the probability of getting spade:

\frac{1}{4}

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

\frac{1}{13} \cdot \frac{1}{4} \cdot \frac{1}{13} \cdot \frac{1}{4} = \frac{1}{2704}

= \frac{1}{2704}