Question

4 5 3 7 89 65Each time, you pick one card randomly and then put it back.What is the probability that the number on the card you pickfirst time is odd and the number on the second card you take isa multiple of 2? Keep your answers in simplified improperfraction form.Enter the answer

Answer 1

We have a total of 8 cards, where 3 of them are a multiple of 2, and 5 is an odd number. Consider that event A represents the probability of picking an odd number and event B is picking a multiple of 2. We know that the events are independent (because we put the cards back), therefore the probability of A and B can be expressed as

`P(A\text{ and }B)=P(A)\cdot P(B)`

Where

`\begin{gathered} P(A)=(5)/(8) \\ \\ P(B)=(3)/(8) \end{gathered}`

Therefore

`P(A\text{ and }B)=(5)/(8)\cdot(3)/(8)=(15)/(64)`

The final answer is

`P(A\text{ and }B)=(15)/(64)`