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.
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?
1 answer