Question

Shruti and pooja randomly choose a colour from red orange and yellow what is the probability that both shows red orange

Answer 1

P(getting red and orange)=2/3

Answer 2

$\bold{\frac{2}{3}}$ is  the probability that both shows orange and red.

Given:

Sruti and Pooja choose a colour and the available colours  are contains red, orange and yellow

To find:

Probability that both shows orange and red = ?

Solution:

Total no of colours  = 3

Hence n(S) = 3

Let A be the probability of choosing orange

$\begin{array}{l}{n(A)=1} \\ {P(A)=\frac{n(A)}{n(S)}=\frac{1}{3}}\end{array}$

Let B be the probability of choosing red

$\begin{array}{l}{n(B)=1} \\ {P(B)=\frac{n(B)}{n(S)}=\frac{1}{3}}\end{array}$

$\begin{aligned} \mathrm{P}(\mathrm{A} \cup \mathrm{B}) &=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B}) \\ &=\frac{1}{3}+\frac{1}{3} \\ &=\frac{2}{3} \end{aligned}$

Probability that both both shows orange and red is $\bold{\frac{2}{3}.}$