A coin is tossed and a dice is rolled.
10.1 Represent the above scenario in a tree diagram. (2)
10.2 How many different possible outcomes are there? (1)
10.3 What is the probability of getting a tail and rolling a prime number?
To create a tree diagram for this scenario, we start with the coin toss and then branch out to represent the two possible outcomes (heads and tails). For each outcome, we then branch out again to represent the six possible outcomes of rolling a dice (numbers 1-6).
Here is the tree diagram:
Coin Toss
/ \
H T
/ \ / \
1 2 1 2
/ \ / \
3 4 3 4
/ \ / \ / \
5 6 5 6 5 6
10.2 To find the number of different possible outcomes, we multiply the number of outcomes for each event. In this case, there are 2 outcomes for the coin toss and 6 outcomes for the dice roll. Therefore, the total number of different possible outcomes is 2 × 6 = 12.
10.3 To find the probability of getting a tail (1 outcome) and rolling a prime number (3 outcomes), we multiply the probabilities of each event. The probability of getting a tail is 1/2, and the probability of rolling a prime number is 3/6. Therefore, the probability of getting a tail and rolling a prime number is (1/2) × (3/6) = 3/12 = 1/4.
Step 1: Draw a vertical line to represent the coin toss.
Step 2: Label the two branches that come out of the line as "Head" and "Tail" to represent the two possible outcomes of the coin toss.
Step 3: From the "Head" branch, draw three horizontal lines to represent the possible outcomes of rolling a dice after getting a Head. Label these lines as "1", "2", and "3" to represent the three possible outcomes of rolling a dice.
Step 4: Repeat Step 3 for the "Tail" branch, labeling the three horizontal lines as "4", "5", and "6" to represent the three possible outcomes of rolling a dice after getting a Tail.
Coin
/ \
/ \
Head / \ Tail
/ \ / \
/ \ / \
1 4 2 5
/ \ / \ / \ / \
/ \ / \ / \ / \
2 5 3 6 4 1 5 2
/ \ / \ / \ / \ / \ / \ / \ / \
3 6 4 1 5 2 3 6 4 1 3 6 2 4 1 3 6
10.2 There are a total of 12 different possible outcomes.
10.3 To calculate the probability of getting a tail and rolling a prime number, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
Favorable outcomes:
- Getting a tail: There are 6 possible outcomes (4, 5, 6, 4, 5, 6).
- Rolling a prime number: There are 3 possible outcomes (2, 3, 5).
Therefore, the number of favorable outcomes is 6.
Total possible outcomes:
Since there are 12 total possible outcomes, the probability is calculated as:
Probability = Number of favorable outcomes / Total possible outcomes = 6/12 = 0.5
So, the probability of getting a tail and rolling a prime number is 0.5 or 50%.