Question

if 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities. enter your answers as fractions or as decimals rounded to 3 decimal places. part 1 of 3 (a) both are spades. p(both are spades) = 0.059 part 2 of 3 (b) both are the same color. p(both are the same color) = 0.490 part: 2 / 3 part 3 of 3 (c) both are kings. p(both are kings) =

Explanation:

Step1: Determine number of kings

A standard deck has 4 kings.

Step2: Calculate probability of first king

Probability of first card being a king: $\frac{4}{52}$.

Step3: Calculate probability of second king

After drawing one king, 3 kings left and 51 cards left. Probability: $\frac{3}{51}$.

Step4: Multiply probabilities

$P(\text{both are kings}) = \frac{4}{52} \times \frac{3}{51} = \frac{12}{2652} = \frac{1}{221} \approx 0.004525$. Rounded to 3 decimal places: 0.005.

Answer:

0.005