Question

lesson plans mathematics day 3 probabilities from a venn diagram: worksheet 1. sort the number cards into the venn diagram 3 5 10 7 9 12 15 odd numbers prime numbers 10 9 3 12 15 5 7 numbers are chosen at random. a. find the probability of selecting an odd number. b. find the probability of selecting a prime number. c. find the probability of selecting a number that is prime and odd. d. find the probability of selecting a number that is not odd or prime. 2. the venn diagram shows information about if students like cricket and rugby. students are selected at random. cricket rugby 15 35 27 12 a) find the probability that the student selected like cricket and rugby. b) find the probability that the student selected doesn’t like either sport. © state of victoria (department of education), 2021

Explanation:

Problem 1a: Probability of selecting an odd number

Step 1: Identify total number of numbers

There are 7 numbers: 3, 5, 10, 7, 9, 12, 15. So total outcomes \( n = 7 \).

Step 2: Identify odd numbers

Odd numbers are 3, 5, 7, 9, 15. So number of odd numbers \( m = 5 \).

Step 3: Calculate probability

Probability \( P(\text{odd})=\frac{m}{n}=\frac{5}{7} \).

Step 1: Recall total number of numbers

Total numbers \( n = 7 \).

Step 2: Identify prime numbers

Prime numbers (numbers greater than 1 with no divisors other than 1 and itself) are 3, 5, 7. So number of prime numbers \( m = 3 \).

Step 3: Calculate probability

Probability \( P(\text{prime})=\frac{m}{n}=\frac{3}{7} \).

Step 1: Recall total number of numbers

Total numbers \( n = 7 \).

Step 2: Identify numbers that are prime and odd

Numbers that are both prime and odd: 3, 5, 7. So number of such numbers \( m = 3 \).

Step 3: Calculate probability

Probability \( P(\text{prime and odd})=\frac{m}{n}=\frac{3}{7} \).

Answer:

\(\frac{5}{7}\)

Problem 1b: Probability of selecting a prime number