Respuesta :
Answer:
0.1433
Step-by-step explanation:
All possibilities:
The total number of different sequences in 40 rolls of a die is [tex]6^{40}[/tex]
Exactly five 1s in 40 rolls:
The 1s may occur at any 5 rolls among 40. The number of ways of exactly five 1s occuring is therefore, equivalent to number of ways of selecting 5 fruits from 40 distinct fruits which is ⁴⁰C₅ ways. These 5 rolls have a fixed outcome 1. Other 35 rolls each have 5 possible outcomes : 2 or 3 or 4 or 5 or 6. So, the number of possible sequences of outcomes on other 35 rolls of the die is [tex]5^{35}[/tex].
⇒The total number of different sequences having exactly five 1s in 40 rolls of a die is (⁴⁰C₅)×([tex]5^{35}[/tex])
∴The fraction of the total number of sequences having exactly five 1s is [tex]\frac{(⁴⁰C₅)×([tex]5^{35}[/tex])}{[tex]6^{40}[/tex]}[/tex] ≈ 0.1433
