Question

one card is drawn and then replaced. a second card is then drawn. what is the probability that the first card is \b\ and the second card is \i\?

cards: p, r, o, b, a, b, i (top row); l, i, t, i, e, s (bottom row)

a) \\(\frac{1}{26}\\) b) \\(\frac{5}{169}\\) c) \\(\frac{6}{26}\\) d) \\(\frac{6}{169}\\)

Explanation:

Step1: Count total cards

Total cards: \(7 + 6 = 13\) (first row 7, second row 6).

Step2: Probability of first card "B"

Number of "B" cards: 2. Probability \(P(B) = \frac{2}{13}\).

Step3: Probability of second card "I"

Number of "I" cards: 3. Probability \(P(I) = \frac{3}{13}\).

Step4: Multiply probabilities (independent events)

\(P(B \text{ and } I) = \frac{2}{13} \times \frac{3}{13} = \frac{6}{169}\).

Answer:

D. \(\frac{6}{169}\)