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, l, i, t, i, e, s options: a) 1/26, b) 5/169, c) 6/26, d) 6/169

Explanation:

Step1: Calculate the probability of drawing 'B' first

There are 13 cards in total, and there are 2 'B' cards.
The probability of drawing a 'B' is \(P(B)=\frac{2}{13}\)

Step2: Calculate the probability of drawing 'I' second

Since the card is replaced, there are still 13 cards. There are 3 'I' cards.
The probability of drawing an 'I' is \(P(I)=\frac{3}{13}\)

Step3: Calculate the combined probability

Since the two events are independent (because of replacement), we use the formula \(P(A\cap B)=P(A)\times P(B)\)
\(P(B\cap I)=\frac{2}{13}\times\frac{3}{13}=\frac{6}{169}\)

Answer:

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