Question

When randomly choosing 2 cards from a deck of cards without replacement what is the probability of choosing a club and then a heart

Answer 1

Answer:

Hence, the total probability(P) of randomly choosing 2 cards from a deck of cards without replacement such that the first card is club and then a heart is: 0.06373.

Step-by-step explanation:

We know that in a deck of 52 playing cards the suits are divided into 4:

" Heart, Club,Diamond and Spade"

i.e. there are total 13 cards each which are Heart, Club,Diamond and Spade.

Hence, the probability of choosing the first card to be Club out of total 52 playing cards is:

$P_{1}=\dfrac{\binom{13}{1}}{\binom{52}{1}}$

similarly the probability of choosing second card to be Heart out of 51 playing cards  is:

$P_{2}=\dfrac{\binom{13}{1}}{\binom{51}{1}}$

Hence, the total probability(P) of randomly choosing 2 cards from a deck of cards without replacement such that the first card is club and then a heart is:

$P=P_{1}+P_{2}$

Hence, $P=0.06373$