Question

Suppose a deck of 52 cards is shuffled and the top two cards are dealt.

Assuming each of these pairs has the same chance, calculate:

b) the chance that the first card is an ace;

c) the chance that the second card is an ace (explain your answer by a symmetry argument as well as by counting);

please answer question C based on B in detail. Better to write down the answer step by step, thank you

Answer 1

b) chance that the first card is an ace =(4/52 )=1/13 (As there are 4 ace in 52 cards)

c) here from symmetry argument ; as we do not have prior information therefore each card has same probability of being ace. Hence proability that 2nd card is ace =4/52 =1/13

from counting :

P(2nd card is ace)=P(first card not ace and 2nd card is ace)+P(first card ace and 2nd card is ace)

=(48/52)*(4/51)+(4/52)*(3/51) =(4/52)*(48/51+3/51)=(1/13)*1 =1/13