Answer:
![Pr = (1)/(6)](https://img.qammunity.org/2022/formulas/mathematics/high-school/4uop2n365rpwgabrcqmrh44zp77nfpwdea.png)
Explanation:
Given
![S = \{1,2,3,4,5\}](https://img.qammunity.org/2022/formulas/mathematics/high-school/8h7ytoe3s4bgohxhdix4hkcu0czx8qwwo2.png)
![n = 5](https://img.qammunity.org/2022/formulas/mathematics/college/xnqjpd3wbza4ikdn8ewoq25z6zhltfh8ao.png)
Required
Probability the third term is 3
First, we calculate the possible set.
The first must be prime (i.e. 2, 3 and 5) --- 3 numbers
![2nd \to 4\ numbers](https://img.qammunity.org/2022/formulas/mathematics/high-school/m4hobz5q0vk2u9kq3n3n07rpn8jiuh6eob.png)
![3rd \to 3\ numbers](https://img.qammunity.org/2022/formulas/mathematics/high-school/o8u79cbbug7sxnkfemb0gphnsip86cv1hz.png)
![4th \to 2\ numbers](https://img.qammunity.org/2022/formulas/mathematics/high-school/6v3p9lvqzlba83k7uwe71r4bp376k8tsbb.png)
![5th \to 1\ number](https://img.qammunity.org/2022/formulas/mathematics/high-school/rvig4rki7cwv45vhp750clxxe3w19zsoz0.png)
So, the number of set is:
![S = 3 * 4 * 3 * 2 * 1](https://img.qammunity.org/2022/formulas/mathematics/high-school/va0gdvw7ja6szeyx1okyj1w5vp2fqzqjk3.png)
![S = 72](https://img.qammunity.org/2022/formulas/mathematics/high-school/apsdvxpxm4cu8y9125tzt40r9fv6ikyf0h.png)
Next, the number of sets if the third term must be 2
i.e. 1 or 5
---- i.e. remove the already selected first term and the 3rd the compulsory third term
i.e. the digit 2
![4th \to 2\ numbers](https://img.qammunity.org/2022/formulas/mathematics/high-school/6v3p9lvqzlba83k7uwe71r4bp376k8tsbb.png)
![5th \to 1\ number](https://img.qammunity.org/2022/formulas/mathematics/high-school/rvig4rki7cwv45vhp750clxxe3w19zsoz0.png)
So
![r = 2 * 3 * 1 * 2 * 1](https://img.qammunity.org/2022/formulas/mathematics/high-school/8o41bgad6ulj7p7fp4aayy0663l6zexnb1.png)
![r = 12](https://img.qammunity.org/2022/formulas/mathematics/college/2faqpsfyh7bqjythnfn2tavzbqpmhmcpnc.png)
So, the probability is:
![Pr = (r)/(S)](https://img.qammunity.org/2022/formulas/mathematics/high-school/31u9j6qhtfmrxry7t1x7h5ocarob0znk19.png)
![Pr = (12)/(72)](https://img.qammunity.org/2022/formulas/mathematics/high-school/bfy76uhgrdqxfswwj9154g4r9urp3kzvaf.png)
![Pr = (1)/(6)](https://img.qammunity.org/2022/formulas/mathematics/high-school/4uop2n365rpwgabrcqmrh44zp77nfpwdea.png)