1. Tardigrade
  2. Question
  3. Mathematics
  4. A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Then P(G), when G is the event that a number greater than 3 occurs on a single roll of the die, is ldots K . .. Here, K refers to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Then $P(G)$, when $G$ is the event that a number greater than 3 occurs on a single roll of the die, is $\ldots K . .$. Here, $K$ refers to

Probability

Solution:

Given that, probability of each odd number is twice as likely to occur as each even number i.e.,
$P(O)=2 P(E)$
When a die is rolled, then the sample is $S$
Now,
$S=\{1,2,3,4,5,6\}$
$P(O)=\frac{4}{6}=\frac{2}{3}$
i.e., $P(F)=\frac{1}{2}\left(\frac{2}{3}\right)=\frac{2}{6}=\frac{1}{3}$
Now, $G$ is the event greater than 3
$\therefore$ Number are $4, 5, 6$
$P(G) =2 \cdot P(E) \cdot P(O) $
$=2\left(\frac{1}{3}\right)\left(\frac{2}{3}\right)=\frac{4}{9}$