Determine whether the event is independent or dependent:
Rolling 5 on a die and flipping tails on a coin.
Answer
Independent.
Flipping heads on a coin and then flipping tails on that same coin.
Drawing a king from a deck of cards and then, without replacing the king, drawing a queen from the same deck of cards.
Dependent.
Using the formal definition of independence, determine whether events A and B are independent or dependent when we roll two dice.
Event A: Rolling 1 on the first die.
Event B: The dice summing to 7.
Since p(A) × p(B) = p(A and B), the events are independent.
Using the formal definition of independence, determine whether events A and B are independent or dependent when we flip three coins.
Event A: The first two coins are heads.
Event B: There are at least two heads among the three coins.
The table below shows the sample space and the favorable outcomes for each event:
We have:
Since p(A) × p(B) ≠ p(A and B), the events are dependent. Catch you on the flip side.
Using the formal definition of independence, determine whether events A and B are independent or dependent.
Given two spinners (this sort of thing) that each have the numbers 1, 2, and 3 (in place of the colors), we spin two numbers.
Event A: Spinning an odd number on the first spinner.
Event B: The sum of the two numbers being odd.
Okay, so you ready to take this exercise for a spin? It even still has that "new problem smell"...
Here's the sample space. The numbers down the side show up on the first spinner; the numbers across the top show up on the second.
Two out of the three numbers on the first spinner are odd (1 and 3), so .
Now for the sum.
From the table, we see that .
Also, , as we can see:
Since p(A) × p(B) ≠ p(A and B), the events are dependent.
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, as we can see: