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\? a $\frac{1}{26}$ b $\frac{5}{169}$ c $\frac{6}{26}$ d $\frac{6}{169}$

Explanation:

Step1: Calculate probability of drawing 'B' first

There are 13 cards in total, and 2 'B's. So the probability of drawing 'B' on the first - draw, $P(B_1)=\frac{2}{13}$.

Step2: Calculate probability of drawing 'I' second

Since the card is replaced, there are still 13 cards in total, and 3 'I's. So the probability of drawing 'I' on the second - draw, $P(I_2)=\frac{3}{13}$.

Step3: Use the multiplication rule for independent events

Since the two draws are independent events, the probability that the first card is 'B' and the second card is 'I' is $P = P(B_1)\times P(I_2)$.
$P=\frac{2}{13}\times\frac{3}{13}=\frac{6}{169}$

Answer:

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