Anumber is chosen at random from 1 to 10. find the probabilty of not selecting a multiple of 3

a. Sample space = { (t₁ , t₂ ) | 0 < t₁ < T , 0 < t₂ < T }

b.A₁ = { t₂ < t₁ < t₂ + a₂ }

  A₂ = { t₁ < t₂ < t₁ + a₁ }

  if t₁ - t₂ < a₂ , t₂ - t₁ < a₁

c. A₃ = { t₂ + a₂ < t₁ < t₂ + a₂ + 1 }

   A₄ = { t₁ + a₁ < t₂ < t₁ + a₁ + 1 }

Step-by-step explanation:

As given,

A train begins crossing the road at time t₁

The car begins crossing the track at time t₂

where 0 < t₁ < T and 0 < t₂ < T

a.)

Sample space = { (t₁ , t₂ ) | 0 < t₁ < T , 0 < t₂ < T }

b.)

Given that -

The train takes a₁ seconds to cross the road

The car takes a₂ seconds to cross the track.

So, The set that correspond to collision is

A₁ = { t₂ < t₁ < t₂ + a₂ }

A₂ = { t₁ < t₂ < t₁ + a₁ }

if t₁ - t₂ < a₂ , t₂ - t₁ < a₁

c)

The set that corresponds to a collision is missed by 1 second or less is -

A₃ = { t₂ + a₂ < t₁ < t₂ + a₂ + 1 }

A₄ = { t₁ + a₁ < t₂ < t₁ + a₁ + 1 }