Questions: Suppose one card is drawn at random from a standard deck, Answer each part, Urite your answers as fractions. (a) Uhat is the probability that the card drawn is a face card? (b) 4 inet is the probability that the card drawn is a dimmond? (6) Yinat is thee probability that the card dravin is a face card or a diamand?

Solution Steps

A standard deck has 52 cards.

There are 12 face cards in a standard deck (3 face cards per suit: Jack, Queen, King, and there are 4 suits). The probability $P(\text{Face card})$ is: $$P(\text{Face card}) = \frac{12}{52} = \frac{3}{13}.$$

There are 13 diamonds in a standard deck. The probability $P(\text{Diamond})$ is: $$P(\text{Diamond}) = \frac{13}{52} = \frac{1}{4}.$$

To find the probability of drawing a face card or a diamond, we use the formula for the union of two events: $$P(\text{Face card or Diamond}) = P(\text{Face card}) + P(\text{Diamond}) - P(\text{Face card and Diamond}).$$ There are 3 face cards that are also diamonds (Jack, Queen, King of diamonds). Thus: $$P(\text{Face card and Diamond}) = \frac{3}{52}.$$ Substituting the values: $$P(\text{Face card or Diamond}) = \frac{12}{52} + \frac{13}{52} - \frac{3}{52} = \frac{22}{52} = \frac{11}{26}.$$

Final Answer