# A spinner for a board game has the numbers 24, 22, 54, 36, 18, 10, 12 & 64 on it. What is the probability that the spinner will land on a multiple of 3 & 4?

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We can first first try to prime factorize the given numbers:

24= 2*2*2*3

22` ` = 2* 11

54 = 2 * 3 * 3 * 3

36 = 2* 2* 3 * 3

18 = 2 * 3 * 3

10= 2 * 5

12 = 2 * 2 * 3

64 = 2* 2* 2* 2 *2*2

Hence, the numbers that is both multple of 3 and 4 are 24,36, and 12.

There are 8 number in all, and 3 of them are multiples of 3 and 4.

So, **the probability that the spinner will land on a multiple of 3 and 4 is 3/8 or 37.5%**.

Multiples of 3 and 4 are: 12, 24, 36. All other numbers are not multiples of both 3 and 4 (e.g. 64 is multiple of 4 but not of 3).

So probability that the spinner will land on multiple of 3 and 4 is *number of multiples of 3 and 4* divided by *number of all numbers.*` `

So there are 3 multiples of 3 and 4 out of 8 possible numbers.

**Hence, the probability of the spinner landing on a multiple of 3 and 4 is**

`P=3/8=0.375`

Lest S be sample space

S={10,12,18,22,24,36,54,64}

E= number multiple of 3 and 4 i.e multiple of 12={12,24,36}

n(S)=8

n(E)=3

P(E)=probability of E=3/8=.375