### Probability Question 9

#### Question 9 - 30 January - Shift 1

If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is through five times, then the probability that the product of the outcomes is positive, is :

(1) $\frac{881}{2592}$

(2) $\frac{521}{2592}$

(3) $\frac{440}{2592}$

(4) $\frac{27}{288}$

## Show Answer

#### Answer: (2)

#### Solution:

#### Formula: Probability of occurrence of an event, Selection of an event

Either all outcomes are positive or any two are negative.

Now, $p=P($ positive $)=\frac{3}{6}=\frac{1}{2}$

$q=P($ negative $)=\frac{2}{6}=\frac{1}{3}$

Required probability

$ \begin{gathered} ={ }^{5} C_5(\frac{1}{2})^{5}+{ }^{5} C_2(\frac{1}{3})^{2}(\frac{1}{2})^{3}+{ }^{5} C_4(\frac{1}{3})^{4}(\frac{1}{2})^{1} \\ =\frac{521}{2592} \end{gathered} $

$\therefore \quad$ Option (2) is correct.