Question

In throwing a fair die, following are the probabilities of getting each face.
1 - k
2 - 2k
3 - 2k
4 - 3k
5 - $3k^2$
6 - $7k^2+k$
Value of 10k = ___

Answer 1

We know that the sample space of the experiment ‘throwing a die’ is {1, 2, 3, 4, 5, 6}
If the die is fair, all the faces have equal chances. But the probabilities are different in this case.
Probabilities of each face is given in terms of k. We want to find the value of k. What should be the relation we look at to find the value of k?
If we add all the probabilities we should get 1, because the probability of sample space is 1.
$\Rightarrow$ k+2k+2k+ 3k+ $3k^2+(7k^2+k)$ = 1
$\Rightarrow$ $10k^2$ + 9k - 1 = 0
$\Rightarrow$ k = - or $k=\frac{1}{10}$
Since probability can’t be negative $k=\frac{1}{10}$
$\Rightarrow$ 10k = 1