Answer: [tex]\dfrac{2}{15}[/tex]
Step-by-step explanation:
Given : Number of questions on sport = 3
Number of questions on General Knowledge = 3
Number of questions on science = 4
Each question printed on separate card , Total cards = 10
Number of ways to select any 2 card out of 10 =[tex]C(10,2)=\dfrac{10!}{2!(10-2)!}=\dfrac{10\times9\times8!}{2\times8!}=45[/tex] →Total outcomes
Number of ways to select any 2 card out of 4 =[tex]C(4,2)=\dfrac{4!}{2!(4-2)!}=\dfrac{4\times3\times2!}{2\times2!}=6[/tex] → Favorable outcomes
Now , the probability of John selecting 2 question on science = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{6}{45}=\dfrac{2}{15}[/tex]
Hence, the required probability is [tex]\dfrac{2}{15}[/tex] .
