Question

A dice is rolled three times. Let E₁ denotes the event of

getting a number larger than the previous number each time

and E₂ denotes the event that the numbers (in order) form an

increasing AP then –

• A. P(E₂) ³ P(E₁)
• B. P(E₂Ē E₁) = 3/10
• C. P(E₂/E₁) = 1/36
• D. P(E₁) = $\frac { 10 } { 3 }$ P(E₂)

Answer 1

Answer: (D)

P(E₁) = $\frac { 10 } { 3 }$ P(E₂)

Answer 2

P(E₁) = $\frac { { } ^ { 6 } \mathrm { C } _ { 3 } } { 216 } = \frac { 5 } { 54 }$

P(E₂) = $\frac { 4 + 2 } { 216 } = \frac { 1 } { 36 }$

E₁ Ē E₂ = E₂

\ P(E₁ Ē E₂) = P(E₂) = 1/36

P(E₂/E₁)= $\frac { P \left( E _ { 1 } \cap E _ { 2 } \right) } { P \left( E _ { 1 } \right) }$ = $\frac { 1 / 36 } { 5 / 54 } = \frac { 54 } { 180 } = \frac { 3 } { 10 }$