Question

2 cards are drawn without replacement from a standard deck. draw a venn diagram that relates to the following:

1. Both cards are from the same suit

2. Both cards have the same rank

3. One card is a face card and the other card is a number card

4. Both cards are from a red suit

Answer 1

2

since there are 52 cards in a deck

1)
P(both cards of same suit, when drawn without replacement) = (13/52) * (12/51) * 4 = 0.2352
{multiplied by 4 because there are 4 suits)

2)

There are 13 units in the deck, with 4 cards of the same unit per each unit. So, drawing a given unit has a probability of 4/52=1/13. Once a card of a certain unit is drawn, there are just 3 cards of the same unit left, so the probability of drawing the second of the same unit is 3/51=1/17. Since there are 13 units, this needs to be multiplied by the number of units, that is 13.
P(both cards having same rank, when drawn without replacement) = (4/52)*(3/51)*13 = 0.0588

3)
P(1 card is face card and other is a number card) = (16/52)*(36/51) = 0.2172
{ we know there are 16 face cards and 36 non face cards)

4)
P(both cards from red suit) = (26/52)(25/51) = 0.2451 (since, there are 13 hearts and 13 diamond)