Calculating Dependent Probability of Sequential Events
To solve this problem, we need to calculate the probability of two events happening one after the other without replacement, which is a dependent probability scenario.
The two events are:
1. Picking a card with the number 1 on it.
2. Picking a card with an even number on it (without replacing the first card).
First, let's calculate the probability of the first event:
There are 3 cards, and only one card has the number 1 on it. So, the probability of picking the number 1 is:
P(1) = 1/3
Now, assuming you picked the card with the number 1 on it, there are now 2 cards left.
The second event is picking an even number, and among the remaining 2 cards (since the first card is not replaced), there is only one even number (which is number 2). So, the probability of picking an even number after picking number 1 is:
P(even | 1) = 1/2
To find the overall probability of both events happening in succession, we multiply the probabilities of each individual event:
P(1 and then an even) = P(1) * P(even | 1)
= (1/3) * (1/2)
= 1/6
Therefore, the probability of picking a 1 and then picking an even number is 1/6.
