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You spin the spinner once. $3,4,5,6,7,8$ What is $P(\text{odd or prime})$ ? Write your answer as a percentage.

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Probability of mutually exclusive events and overlapping events

Full solution

Q. You spin the spinner once.

3,4,5,6,7,8

What is

P(\text{odd or prime})

? Write your answer as a percentage.

Identify numbers on spinner: Identify the total numbers on the spinner and the numbers that are odd or prime. $\newline$ Total numbers = $345678$ $\newline$ Odd numbers = $(345678 + 1) / 2 = 172839$ $\newline$ Prime numbers = (Using approximation formula for primes less than $n$ , $\pi(n) \approx n / \log(n)$ ) $\newline$ Prime numbers $\approx 345678 / \log(345678) \approx 24512$
Calculate odd and prime numbers: Calculate the union of odd and prime numbers. $\newline$ Since all prime numbers except $2$ are odd, the union is just the odd numbers plus $2$ if it's not included. $\newline$ Union of odd and prime = $172839$ (since $2$ is even and not included in odd count)

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