barbara placed the numbered cards shown below into a bag. if barbara chooses a card, does not replace it…

barbara placed the numbered cards shown below into a bag. if barbara chooses a card, does not replace it, then chooses another, what is the probability that barbara will choose an even number and then a multiple of 3? 3 4 1 9 4 5 6 3

barbara placed the numbered cards shown below into a bag. if barbara chooses a card, does not replace it, then chooses another, what is the probability that barbara will choose an even number and then a multiple of 3? 3 4 1 9 4 5 6 3

Answer

Explanation:

Step1: Count total, even, and multiple - of - 3 cards

There are 8 cards in total. Even numbers are 4, 4, 6, so there are 3 even - numbered cards. Multiples of 3 are 3, 3, 9, 6, so there are 4 multiples of 3.

Step2: Calculate probability of choosing an even - numbered card first

The probability of choosing an even - numbered card first, $P(E_1)=\frac{3}{8}$.

Step3: Calculate probability of choosing a multiple of 3 second (without replacement)

After choosing an even - numbered card first, there are 7 cards left. The probability of choosing a multiple of 3 second, given that an even - numbered card was chosen first, $P(M_2|E_1)=\frac{4}{7}$.

Step4: Calculate the joint probability

By the multiplication rule for dependent events $P(E_1\cap M_2)=P(E_1)\times P(M_2|E_1)=\frac{3}{8}\times\frac{4}{7}=\frac{3\times4}{8\times7}=\frac{12}{56}=\frac{3}{14}$.

Answer:

$\frac{3}{14}$