Question

A counter is chosen at random from a bag of yellow and red counters, and a spinner with odd and even numbers on is spun. What probabilities should replace A, B, C and D on the tree diagram below? Give each of your answers as a decimal. Colour of counter Number on spinner

Answer 1

To determine the probabilities on the tree diagram, divide the number of counters of a particular color by the total number of counters in the bag, and multiply it by the probability of spinning the corresponding number.

Step-by-step explanation:

To determine the probabilities on the tree diagram, we need to calculate the probability of each branch. Let's assume that there are k yellow counters and n total counters in the bag.

A branch on the tree diagram represents the probability of selecting a particular color of counter and spinning a particular number on the spinner. The probabilities on each branch are calculated by dividing the number of counters of that color by the total number of counters in the bag, and multiplying it by the probability of spinning the corresponding number on the spinner. For example, if there are m yellow counters in the bag:

1. The probability of selecting a yellow counter and spinning an odd number is (m/n) * (1/2).
2. The probability of selecting a yellow counter and spinning an even number is (m/n) * (1/2).
3. The probability of selecting a red counter and spinning an odd number is ((n-m)/n) * (2/3).
4. The probability of selecting a red counter and spinning an even number is ((n-m)/n) * (1/3).