Question

Two cards are chosen at random from a deck of $52$playing cards. What is the probability that they

(a) are both aces?

(b) have the same value?

Short answer

$$\begin{gathered} \left(a\right)0.0045 \\ \left(b\right)0.059 \end{gathered}$$

Step-by-step solution

Given Information.

Two cards are chosen at random from a deck of $52$playing cards.

Part (a) Explanation.

$$\begin{gathered} \text{P((bothaces)=P(firstace)}{}^{*}P(secondace) \\ =(4/52)*(3/51) \\ =0.0045 \end{gathered}$$

Part (b) Explanation.

$$\begin{gathered} P\left(\right(bothsamevalue)=[Chooseavalue\left]{}^{*}P\right(firstcard\left){}^{*}P\right(secondcardwithsamevalue) \\ =(13C1)*(4/52)*(3/51) \\ =13*(1/13)*(1/17) \\ =0.059 \end{gathered}$$