Question

(3 points) A deck consists of cards with 5 suits labelled A to E and numbered ranks from 1 to 6. Each card is equally likely to be drawn. Suits A to C are red. Suits D to E are blue. A card is drawn at random from this deck. What is the probability of it being suit A? 5/30 What is the probability of it being suit A given that it is red? What is the probability of it being suit A given that it is blue? What is the probability of it being suit A given that it has rank 1? What is the probability of it having a rank less than or equal to 2? What is the probability of it having a rank less than or equal to 2 given it has a red suit? What is the probability of it having a rank less than or equal to 2 given it has a rank less than or equal to 4? What is the probability of it having a rank less than or equal to 4 given it has a rank less than or equal to 2?

Answer 1

1)

P(suit A ) =1/5 (since A is one of 5 suits)

2)

P(Suit A |red )=1/3

3)

P(suit A|blue )=0

4)P(suit A| rank 1) =1/5

5)

P(rank less than or equal to 2) =2/6 =1/3

6)P(rank less than or equal to 2 given red suit) =1/3

7)P(<=2 |<=4) =2/4=1/2

8) P(<=4 |<=2) =1