Question

You flip a coin and then roll a 6-sided number cube (a die).

a. When finding the probability, does it matter whether you roll the die or flip the coin first?

b. Is there more than one way to draw a tree diagram for this problem? If so, does that change the likelihood that any outcome will occur?

c. Draw the shape of the tree diagram that you would use.

d. How many outcomes are there? List them.

e. Find the probability of rolling an even number and getting heads.

Answer 1

Answer:

a)  No, it does not matter whether you roll the die or flip the coin first, as these two events are independent of each other, which means they do not affect each other.

b) Yes.

• Let event 1 be flipping a coin and event 2 be rolling a die.
• Let event 1 be rolling a die and event 2 be flipping a coin.

The likelihood that any outcome will occur will not change, as the events are independent.

c) see attached

d)   12 outcomes  (H = head, T = tail, numbers represent the value of the die)

H 1           T 1

H 2          T 2

H 3          T 3

H 4          T 4

H 5          T 5

H 6          T 6

e)  

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

$\implies \sf P(even)=\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}=\dfrac{3}{6}=\dfrac{1}{2}$

$\implies \sf P(head)=\dfrac{1}{2}$

$\implies \sf P(even)\:and\:P(head)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}$