A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. discs are similar in shape a

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14.Probability

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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.

A

$\frac{7}{9}$

B

$\frac{7}{9}$

C

$\frac{7}{9}$

D

$\frac{7}{9}$

Solution

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

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

Standard 11

Mathematics

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