QI) A coin is tossed and a die is rolled. Write the number of outcomes for the sequence of events
(sample space S). Then,
Draw a tree diagram for the sequence of events.
Cannot draw a tree diagram here.
A coin is tossed and a die is rolled. Write the number of outcomes for the sequence of events (sample space S). Then,
Draw a tree diagram for the sequence of events.
To find the number of outcomes for the sequence of events, we need to consider all possible outcomes for each event and multiply them together.
Event 1: Coin toss
The coin can either land on heads (H) or tails (T). So, there are 2 possible outcomes for this event.
Event 2: Die roll
The die has 6 faces numbered 1, 2, 3, 4, 5, and 6. So, there are 6 possible outcomes for this event.
To find the total number of outcomes for the sequence of events, we multiply the number of outcomes for each event together:
Total outcomes = Number of outcomes for Event 1 × Number of outcomes for Event 2
Total outcomes = 2 × 6 = 12
So, the number of outcomes for the sequence of events is 12.
Now, let's draw a tree diagram for the sequence of events:
Coin Toss
/ \
H T
/ \ / \
Die Roll Die Roll Die Roll Die Roll
/ | \ / | \ / | \ / | \
1 2 3 1 2 3 1 2 3 4 5 6
In this tree diagram, the first branch represents the coin toss, with H for heads and T for tails. The second branch represents the die roll, with the numbers 1, 2, 3, 4, 5, and 6. Each set of branches represents a specific outcome of the coin toss and die roll events.
To determine the number of outcomes for the sequence of events, we need to calculate the sample space, which is the set of all possible outcomes of the combined events of tossing a coin and rolling a die.
1) Tossing a coin: There are two possibilities - heads (H) or tails (T).
2) Rolling a die: There are six possibilities - numbers 1 through 6.
To find the number of outcomes for the sequence of events, we multiply the number of outcomes for each event together:
Number of outcomes for tossing a coin (2) * Number of outcomes for rolling a die (6) = 2 * 6 = 12
So, there are 12 possible outcomes in the sample space for this sequence of events.
Now, let's draw a tree diagram to visualize the possible outcomes:
/---- 1
/---- H (heads)
/
Coin
\
\---- T (tails)
\---- 2
....
....
\---- 6
/
Dice
\
\---- 1
....
....
\---- 6
In the tree diagram, the branches represent the possible outcomes of each event. The branches for the coin toss split into "H" and "T", and each branch for the die roll splits into numbers 1 through 6. The endpoints of the branches represent the final outcomes, which are the combined outcomes of the coin toss and die roll.