one card is drawn and then replaced. a second card is then drawn. what is the probability that the first…

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\? p r o b a b i l i t i e s a 1/26 b 5/169 c 6/26 d 6/169

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\? p r o b a b i l i t i e s a 1/26 b 5/169 c 6/26 d 6/169

Answer

Explanation:

Step1: Calculate probability of first - card

There are 13 cards in total. The probability of drawing a 'B' first. Since there are 2 'B's, the probability $P_1=\frac{2}{13}$.

Step2: Calculate probability of second - card

Since the card is replaced, there are still 13 cards. The probability of drawing an 'I' second. Since there are 3 'I's, the probability $P_2 = \frac{3}{13}$.

Step3: Calculate combined probability

For independent events, the combined probability $P = P_1\times P_2=\frac{2}{13}\times\frac{3}{13}=\frac{6}{169}$.

Answer:

D. $\frac{6}{169}$