Question

Let S={$a,b,c$} be the sample space with the associated probabilities satisfying $P(a)=2P(b)$ and $P(b)=2P(c).$Then the value of $P(a)$ is

• A. $\dfrac{1}{5}$
• B. $\dfrac{2}{7}$
• C. $\dfrac{1}{7}$
• D. $\dfrac{1}{6}$
• E. $\dfrac{4}{7}$

Answer 1

Answer: (C)

$\dfrac{1}{7}$

Answer 2

Given data
Sample space, $S=${$a,b,c$}

Let's take probability of a $P(a) = x$

Accordingly $,P(b) = 2P(a) = 2x$

and $P(c) = 2P(b) = 2(2x) = 4x$

We know that sum of all events is one

So, $P(a) + P(b) + P(c) = x + 2x + 4x = 7x = 1$

$⇒x = \dfrac{1}{7}$

So,$P(a) =\dfrac{1}{7}$ (_Ans.)