3 Marks Question

Question 13 Marks

In a survey of $200$ ladies, it was found that $82$ like coffee while $118$ dislike it. From these ladies, one is chosen at random. What is the probability that the chosen lady dislikes coffee?

Answer

Total number of ladies $= 200$
Those who like coffee $= 82$
Those who dislike coffee $= 118$
Possible number of outcimes $= 200$
One lady is chosen at random, then
$i.$ Probability of a lady who dislikes coffee $=\frac{118}{200}=\frac{59}{100}$

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Question 23 Marks

One card is drawn at random from a well$-$shuffled deck of $52$ cards. Find the probability that the card drawn is:
$i.$ A $4$.
$ii.$ A queen.
$iii.$ A black card.

Answer

One card is drawn at random from a deck of well-shuffled deck of $52$ card. Possible outcomes $= 52$
$i.$ Probability of a card being a $4=\frac{4}{52}=\frac{1}{13}$
$ii.$ Probability of a card being a queen $=\frac{4}{52}=\frac{1}{13}$
$iii.$ Probability of a card being a black card $=\frac{26}{52}=\frac{1}{2}$

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Question 33 Marks

A box contains $19$ balls bearing numbers $1, 2, 3, ..., 19$ respectively. A ball is drawn at random from the box. Find the probability that the number on the ball is:
$i.$ A prime number.
$ii.$ An even number.
$iii.$ A number divisible by $3$.

Answer

$19$ ball bearing numbers, $1, 2, 3,.... 19$ Possible outcomes $= 19$ A ball is drawn at random from the box, then
$i.$ Probability of a ball which bears a prime numbers which are $ 2, 3, 5, 7, 11, 13 17$ and $19 = 8$ $=\frac{8}{19}$
$ii.$ Probability of a ball which bears an even number which are $ 2, 4, 6, 8, 10, 12, 14, 16, 18 = 9$ $=\frac{9}{19}$
$iii.$ Probability of a number which bears a number divisible by $3$ which are $3, 6, 9, 12, 15, 18 = 6$ $=\frac{6}{19}$

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Question 43 Marks

In a single throw of two coins, find the probability of getting:
$i.$ Both tails,
$ii.$ At least $1$ tail,
$iii.$ At the most $1$ tail.

Answer

The outcomes when two coins are tossed are $\text{HH, HT, TH}$ and $\text{TT}$.
I.e., total no. of possible outcomes $= 4$
$i.$ Getting both tails means $\text{TT}$.
Number of outcomes with two tails $= 1$
$\therefore \text{P}_{\text{both tails}}=\frac{1}{4}$
$ii.$ Getting at least $1$ tail means $\text{HT, Th}$ and $\text{TT}$.
With at least one tail, total number of outcomes $= 3$
$\therefore\text{P}_{\text{at least 1 tail}}=\frac{3}{4}$
$iii.$ Getting at most $1$ tail means $\text{HH, HT}$ and $\text{TH}$.
The number of outcomes for at most $1$ tail $= 3$
$\therefore \text{P}_{\text{at most 1 tail}}=\frac{3}{4}$

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Question 53 Marks

It is known that a box of $100$ electric bulbs contains $8$ defective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is:
$i.$ Defective?
$ii.$ Non$-$defective?

Answer

In a, box $100$ electric bulb, $8$ are defective.
Then non$-$defective bulbs $= 100 - 8 = 92$
Now possible outcomes $= 100$
$i.$ Probability of a drawn bulb, which is defective $=\frac{8}{100}=\frac{2}{25}$
$ii.$ Probability of a drawn bulb which is non defective $=\frac{92}{100}=\frac{23}{25}$

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Question 63 Marks

A bag contains $4$ white and $5$ blue balls. They are mixed thoroughly and one ball is drawn at random. What is the probability of getting:
$i.$ A white ball?
$ii.$ A blue ball?

Answer

In a bag, there are $4$ ehite and $5$ blue balls, Possible outcomes $= 4 +5 = 9$ One ball is drawn at random, then
$i.$ The probability of a white ball $=\frac{4}{9}$
$ii.$ The probability of a blue ball $=\frac{5}{9}$

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Question 73 Marks

A bag contains $5$ white, $6$ red and $4$ green balls. One ball is drawn at random. What is the probability that the ball drawn is:
$i.$ Green?
$ii.$ White?
$iii.$ Non$-$red?

Answer

In a bag, there are $5$ white, $6$ red and $4$ green balls.
Possible outcomes is $5 + 6 + 4 = 15$
One ball is drawn at random, then
$i.$ Probability of a green ball $=\frac{4}{15}$
$ii.$ Probability of a white ball $=\frac{5}{15}=\frac{1}{3}$
$iii.$ Probability of a non$-$red ball $=\frac{5+4}{15}$
$=\frac{9}{15}=\frac{3}{5}$
$(5$ white and $4$ ghreen balls are non$-$red balls$)$

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