Question

6.1 You roll a die and flip a coin at the same time. Answer the following questions based on this event.

6.1.1 Draw a tree diagram to represent all the outcomes.
6.1.2 What is the probability of getting a 4 and tails?
6.1.3 What is the probability of geting a heads and a number greater than 37
6.2 A two-digit number is formed from digits 5, 6 and 7. These digits may be repeated.
6.2.1 Using a tree diagram, show all the numbers that could be formed.
6.2.2 Find the probability that the number will be odd.
6.2.3 Find the probability that the number will be a multiple of 3.
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Answer 1

To represent the outcomes of rolling a die and flipping a coin, we can create a tree diagram. The probability of getting a 4 and tails is 1/12. The probability of getting heads and a number greater than 3 is 1/4.

Step-by-step explanation:

6.1.1 To represent all the outcomes of rolling a die and flipping a coin, we can create a tree diagram with two branches for each event. The first level will represent the die roll outcomes (1, 2, 3, 4, 5, 6), and the second level will represent the coin flip outcomes (heads, tails). The branches will show all possible combinations of the two events.

6.1.2 The probability of getting a 4 and tails is based on the number of favorable outcomes divided by the total number of possible outcomes. Since there is only one outcome that satisfies both conditions (rolling a 4 and flipping tails), and there are 12 possible outcomes in total (6 die outcomes multiplied by 2 coin outcomes), the probability is 1/12 or approximately 0.0833.

6.1.3 To find the probability of getting heads and a number greater than 3, we first calculate the probability of getting heads, which is 1/2. Then, we calculate the probability of getting a number greater than 3, which is 3/6 or 1/2. Finally, we multiply the two probabilities together to get 1/4 or 0.25.

Learn more about Probability and Tree diagrams