Question

find the indicated probability.
if you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade?
$\frac{1}{13}$
$\frac{11}{26}$
$\frac{1}{2}$
$\frac{15}{26}$

Explanation:

Step1: Define total card count

Total cards in deck: $n(S) = 52$

Step2: Count face cards

Face cards (J/Q/K per suit): $n(F) = 12$

Step3: Count spade cards

Spade suit cards: $n(S_p) = 13$

Step4: Count overlapping cards

Face cards that are spades: $n(F \cap S_p) = 3$

Step5: Apply addition rule

Use $P(F \cup S_p) = P(F) + P(S_p) - P(F \cap S_p)$

$$\begin{align*} P(F \cup S_p) &= \frac{12}{52} + \frac{13}{52} - \frac{3}{52}\\ &= \frac{12+13-3}{52}\\ &= \frac{22}{52}\\ &= \frac{11}{26} \end{align*}$$

Answer:

$\boldsymbol{\frac{11}{26}}$ (Option: $\boldsymbol{\frac{11}{26}}$)