Question

Two cards are drawn at random from a standard deck of 52 cards. The number of aces drawn is counted. Prepare a probability distribution for this random experiment. Hint: Find the probability that no aces are drawn, exactly one ace is drawn, etc.

Answer 1

Solution:
Given in the question
The standard deck has total cards = 52
We need to draw 2 cards and we need to prepare a probability distribution for this random experiment
First, we will calculate the probability that No aces are drawn which can be calculated as
P(No aces are drawn) = (Total number of way to select 2 cards drawn without any aces)/Total no. of way to draw 2 cards out of 52 cards) = 48C2 / 52C2 = 1128/1326 = 0.8507
Second, we will calculate probability that 1 ace is drawn which can be calculated as
P(One ace are drawn) = (Total no. of ways One ace is drawn out of 4 aces)* (Total number of ways another card is drawn except Ace out of 48 cards)/ Total no. of way to draw 2 cards out of 52 cards) = (4C1*48C1)/(52C2) = 192/1326 = 0.1448
Now we will calculate the probability that both aces are drawn which can be calculated as
P(Two aces are drawn) = (Number of ways to select 2 aces out of 4 aces)/ (Number of ways to select 2 cards out of 52 cards) = 4C2/52C2 = 6/1326 = 0.0045
So probability distribution can be written as follows
​​​​​​​

No. of aces	Probability(Number of Aces)
0	0.8507
1	0.1448
2	0.0045