# How tolearn cards for probability

For the understand the numerical based on the probability of playing cards, this formula will help us:-

In n trials of a random experiments, if an event A happens m times, then the probability of happening of A is given by P(A) = m/n.

BY the some examples we can understand the cards for probability:-

Q.1 One card is drawn from a well – shuffled deck of 52 cards. Find the probability of getting

(i) a king of red colour (ii) a face card

(iii) a red face card (iv) the jack of hearts

(v) a spade (vi) the queen of diamonds

Sol. Out of 52 cards, one card can be drawn in 52 ways. So, total number of elementary events = 52

(i) There are two suits of red cards viz. diamond and heart. Each suit contains one king.

Therefore, Favourable number of elementary events = 2 X 1 = 2

Hence, P(a king of red colour) = {2/52} = 1/26

(ii) In a deck of 52 cards: kings, queens and jacks are called face cards. Thus, there are 12 face cards. So, one face card can be chosen in 12 ways. Therefore, Favourable number of elementary events = 12

Hence, P(a face card) = 12/52 = 3/13

(iii) There are two suits of red cards viz. diamond and heart. Each suit contains 3 face cards.

Therefore, Favourable number of elementary events = 2 X 3 = 6

Hence, P(a red dace card) = 6/52 = 3/26

(iv)There is only one jack of hearts

Therefore, Favourable number of elementary events = 1

Hence, P(the jack of hearts) = 1/52

(v) There are 13 cards of spade.

Therefore, Favourable number of elementary events = 13

Hence, P(a spade) = 13/52 = 1/4

(vi) There is only one queen of diamonds.

Therefore, Favourable number of elementary events = 1

Hence, P(the queen of diamonds) = 1/52.

Q.2 Five cards – the ten, jack, queen, king and ace of diamonds, are well – shuffled with their face downwards. One card is then picked up at random.

(i) What is the probability that the card is the queen?

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?

Sol. Out of five cards — the ten, jack, queen, king and ace of diamonds, one card can be drawn in 5 ways. So, total number of elementary events = 5

(i) There is only one queen.

Therefore, Favourable number of elementary events = 1

Hence, P(the queen) = 1/5

(ii) After keeping the queen card aside, we are left with 4 cards. So total number of elementary events now = 4.

(a) There is only one ace

Therefore,Favourable number of elementary events = 1

Hence, P(an ace) = 1/4

(b) There is no card as queen.

Therefore,Favourable number of elementary events = 0

Hence, P(the queen) = 0/4 = 0.