Q81 / 160 · TS EAMCET 2006 · Mathematics

In the random experiment of tossing two unbiased dice let $E$ be the event of getting the sum 8 and $F$ be the event of getting even numbers on both the dice. Then : I. $P(E)=\frac{7}{36}$ II. $P(F)=\frac{1}{3}$ Which of the following is a correct statement?

  • A
    Both I and II are true
  • Correct answer
    B
    Neither I nor II is true
  • C
    I is true, II is false
  • D
    I is false, II is true

Solution

$E=$ Event of getting the sum 8 . $=\{(2,6),(3,5),(4,4),(5,3),(6,2)\}$ and $F=$ Event of getting the even numbers on both the dice. $=\{(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)\}$ $\therefore \quad P(E)=5 \quad$ and $\quad P(F)=6$ also $\quad n(S)=36$ $\therefore \quad P(E)=\frac{n(E)}{n(S)}=\frac{5}{36}$ and $\quad P(F)=\frac{n(F)}{n(S)}=\frac{6}{36}$ $=\frac{1}{6}$ $\therefore \quad$ Neither I nor II is true

Hence, the correct answer is option: 'B'.

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