CARDS PROBABILITY PART 1.pptx

PROBABILITY ON CARDS

1. PROBABILITY Ms. NEHA CHANDRAKANT PATIL Assistant Professor ( Department of Mathematics) Changu Kana Thakur ACS College( Autonomous) , New Panvel

2. Deck of cards is the term used for a set of 52 cards consisting of different types of cards.  There are 4 suits ,13 cards of each suit, consisting of 1 Ace, 3 face cards, and 9 number cards. There are 4 Aces, 12 face cards, and 36 number cards in a 52 card deck. Probability of drawing any card will always lie between 0 and 1. The number of spades, hearts, diamonds, and clubs is same in every pack of 52 cards.

3. 1)What is the probability of drawing a red card from a pack of cards? Solution: Here the event E is drawing a red card from a pack of cards. The total number of outcomes = 52 The number of red cards (13 of each suit) = 13*2= 26 Hence, the probability of drawing a red card is  P(E) = =  

4. 2) Jessica has drawn a card from a well-shuffled deck. Help her find the probability of the card either being red or a King. Solution: Jessica knows here that event E is the card drawn being either red or a King. The total number of outcomes = 52 There are 26 red cards, and 4 cards which are Kings. However, 2 of the red cards are Kings. If we add 26 and 4, we will be counting these two cards twice.

5. Thus, the correct number of outcomes which are favorable to E is 26 + 4 - 2 = 28 Hence, the probability of card being red or king is P(E) =  

6. 3 ) D etermine the probability of the following: ( i )Drawing a Red Queen (ii)Drawing a King of Spades (iii)Drawing a Red Number Card  Solution: let the events E 1 , E 2 , and E 3  be Drawing a Red Queen, Drawing a King of Spades, and Drawing a Red Number Card. The total number of outcomes in every case = 52 ( i ) Drawing a Red Queen There are 4 queens in the cards, of which 2 are red and 2 are black.

7. Hence, the probability of event E 1  occurring is P(E 1 ) = (ii) Drawing a King of Spades There are 13 spade cards , of which 1 is King. Hence, the probability of event E 2  occurring is P(E 2 ) =  

8. (iii)Drawing a Red Number Card There are 9 number cards in each suit and there are 2 suits which are red in color.  There are 18 red number cards. Hence, the probability of event E 3  occuring is P(E 3 ) = =  

9. 4 ) From a shuffled pack of cards, John picks up one card at random. What is the probability of it being a hearts' card? Solution: Here the event E is drawing a heart card from a pack of cards. The total number of outcomes = 52 The number of heart cards = 13 Hence, the probability of drawing a red card is  P(E) = =  

10. 5)From a deck of 52 cards, Justin picks up one at random. What is the probability of it being a red non-face card? Solution: Here the event E is drawing a red non-face card from a pack of cards. The total number of outcomes = 52 The number of red cards = 13 Number of face cards = 3 Total number of red non-face cards= 13-3 = 10 Hence, the probability of drawing a red non-face card is  P(E) = =