you pick a card at random. without putting the first card back, you pick a second card at random. what is…
you pick a card at random. without putting the first card back, you pick a second card at random. what is the probability of picking an odd number and then picking an odd number? simplify your answer and write it as a fraction or whole number.
Answer
Explanation:
Step1: Calculate first - pick probability
There is 1 odd number (3) out of 3 cards. So the probability of picking an odd number on the first pick is $\frac{1}{3}$.
Step2: Calculate second - pick probability
After picking an odd number on the first pick (without replacement), there are 2 cards left and 0 odd numbers left. So the probability of picking an odd number on the second pick given an odd - number was picked first is 0.
Step3: Calculate joint probability
By the multiplication rule for dependent events $P(A\cap B)=P(A)\times P(B|A)$. Here $A$ is the event of picking an odd number first and $B$ is the event of picking an odd number second. So $P=\frac{1}{3}\times0 = 0$.
Answer:
0