Answer: [tex]\frac{5}{16}[/tex]
Step-by-step explanation:
Given: A fair coin is tossed 5 times in a row.
Total outcomes=2×2×2×2×2=32 [total outcomes in a coin is 2]
Let A be the event of getting heads exactly 2 times
Then the favorable outcomes=[tex]^5C_2[/tex]
[tex]=\frac{5!}{2!(5-2)!}=\frac{5\times4\times3!}{2!\times3!}\\=\frac{5\times4}{2}=10[/tex]
Then probablity of getting heads exactly 2 times =
[tex]P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total outcomes}}\\\Rightarrow\ P(A)=\frac{10}{32}\\\\\Rightarrow\ P(A)=\frac{5}{16}[/tex]
