49. Checking independence In which of the following games of chance would you be willing to assume independence of $X$andlocalid="1649903939419" $Y$ in making a probability model? Explain your answer in each case.
(a) In blackjack, you are dealt two cards and examine the total points localid="1649903945891" $X$on the cards (face cards count localid="1649903950298" $10$points). You can choose to be dealt another card and compete based on the total pointslocalid="1649903956461" $Y$ on all three cards.
(b) In craps, the betting is based on successive rolls of two dice. localid="1649903966379" $X$is the sum of the faces on the first roll, and localid="1649903971075" $Y$is the sum of the faces on the next roll.

Given in the question that, In blackjack, are dealt two cards. And then choose to be dealt another card and compete based on the total points $Y$on all three cards.

Handled two cards in blackjack and studied the all-out focus $X$on the cards (face cards check ten focuses). And choose another card to be addressed; thus, on each of the three cards, contend based on the all-out direction $Y$.

Because the second card has been set without replacing the deck with the cards, the events $X$and $Y$cannot be assumed to be independent.

The betting is based on successive rolls of two dice. $X$is the sum of the faces on the first roll, and $Y$is the sum of the faces on the next roll.

Two events $X$and $Y$are independent. Because the faces of both rolls do not influence each other, . There is a probability that the exact number will appear on both rolls.