Question

Riya and Priya are playing a card game. Riya
asks
Priya to pick two random cards from a deck of 52 cards
without
replacement. They have decided that if the
cards drawn by Priya are king
and then
queen, then
Priya will win; otherwise, Riya will win. So, what is the
probability that Priya will win​

Answer 1

Step-by-step explanation:

please mark brainliest to priya

Answer 2

Probability that Priya will win is $\frac{4}{663}$

Given : Priya pick two random cards from a deck of 52 cards

without replacement.

Priya will win if the cards drawn by Priya are king and then queen

To Find : The probability that Priya will win

Solution : Probability that Priya will win is $\frac{4}{663}$

Total number of cards in a deck is 52

Total number of kings in the deck is 4

Probability that Priya will first choose king is

P(A1) = $\frac{Total \hspace{0.1cm} number \hspace{0.1cm}of \hspace{0.1cm} king\hspace{0.1cm} in\hspace{0.1cm} the \hspace{0.1cm}deck}{Total\hspace{0.1cm} number\hspace{0.1cm} of\hspace{0.1cm} cards\hspace{0.1cm} in \hspace{0.1cm}the\hspace{0.1cm} deck}$

= $\frac{4}{52}$

So probability that the card first drawn is king is  $\frac{4}{52}$

Now the second card is drawn without replacement

So total number of cards now left are 51

Total number of queen in the deck is 4

So Probability that Priya will  choose queen is

P(A1) = $\frac{Total \hspace{0.1cm} number \hspace{0.1cm}of \hspace{0.1cm} queen\hspace{0.1cm} in\hspace{0.1cm} the \hspace{0.1cm}deck}{Total\hspace{0.1cm} number\hspace{0.1cm} of\hspace{0.1cm} cards\hspace{0.1cm} in \hspace{0.1cm}the\hspace{0.1cm} deck}$

=  $\frac{4}{51}$

So probability that the second card f drawn is queen is  $\frac{4}{51}$

So probability that Priya will win is P(A1) ×P(A2)

=  $\frac{4}{52}$ ×  $\frac{4}{51}$

=  $\frac{16}{2652}$

=  $\frac{4}{663}$

So probability that Priya will win is $\frac{4}{663}$

#SPJ2