Question

A die 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(E₂Ç E₁) = $\frac { 3 } { 10 }$
• C. P(E₂/ E₁)= $\frac { 1 } { 36 }$
• D. P (E₁) = $\frac { 10 } { 3 }$ P (E₂)

Answer 1

Answer: (B)

P(E₂Ç E₁) = $\frac { 3 } { 10 }$

Answer 2

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

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

E₁ Ç E₂ = E₂

\ P (E₁ Ç E₂) = P (E₂) = 1/ 36

P(E₂ / E₁) = = $\frac { 3 } { 10 }$