A bag contains $9$ discs of which $4$ are red, $3$ are blue and $2$ are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be either red or blue.

Vedclass pdf generator app on play store
Vedclass iOS app on app store

There are $9$ discs in all so the total number of possible outcomes is $9 .$

Let the events $A, \,B, \,C$ be defined as

$A:$ 'the disc drawn is red'

$B:$ 'the disc drawn is yellow'

$C:$ 'the disc drawn is blue'.

The event 'either red or blue' may be described by the set $'A$ or $C'$

since, $A$ and $C$ are mutually exclusive events, we have

$P ( A \text { or } C )= P ( A \cup C )$ $= P ( A )+ P ( C )=\frac{4}{9}+\frac{1}{3}=\frac{7}{9}$

Similar Questions

Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11$, if $5$ appears on the first

Let $A$ and $B$ be independent events such that $\mathrm{P}(\mathrm{A})=\mathrm{p}, \mathrm{P}(\mathrm{B})=2 \mathrm{p} .$ The largest value of $\mathrm{p}$, for which $\mathrm{P}$ (exactly one of $\mathrm{A}, \mathrm{B}$ occurs $)=\frac{5}{9}$, is :

  • [JEE MAIN 2021]

Three ships $A, B$ and $C$ sail from England to India. If the ratio of their arriving safely are $2 : 5, 3 : 7$ and $6 : 11$ respectively then the probability of all the ships for arriving safely is

If $P(A)=\frac{3}{5}$ and $P(B)=\frac{1}{5},$ find $P(A \cap B)$ if $A$ and $B$ are independent events

In a hostel, $60 \%$ of the students read Hindi newspaper, $40 \%$ read English newspaper and $20 \%$ read both Hindi and English newspapers. A student is selected at random. If she reads English newspaper, find the probability that she reads Hindi newspaper.