Question

. A ball is drawn random from a bag containing some balls numbered 10,11,12……….24.
Find the probability of drawing: 5
(i) a ‘23’
(ii) an odd number
(iii) a composite number
(iv) a perfect square
(v) a perfect cube

Answer 1

Step-by-step explanation:

Total number of outcomes = 15

Answer 2

(i) $\frac{1}{15}$

(ii) $\frac{7}{15}$

(iii) $\frac{10}{15}$

(iv) $\frac{1}{15}$

(v) 0

Probability is defined to be prediction of the occurrence of an event on whether it is possible for the event to take place or not.

It comes into picture when the solution to a problem is vague or there is an uncertainty to it.

Probability is the measure of the likelihood of occurrence of an event and is represented by a fraction.

This is because it lies in the range between 0 to 1 including them. If the probability is 0 it means that the event has not occurred at all and 1 implies that the event will surely occur.

It is said to be given as the number of possible or favourable outcomes divided by the total number of outcomes that are possible. Here, the term outcomes refers to the outcome of an event if it occurs.

$P(A)=\frac{No.\;of\;favourable\;outcomes\;to\;A}{Total\;no.\;of\;outcomes}$

where P(A) represents the probability of an event A.

Thus, there will be a total set of possibilities out of which the occurrence of the event gives the probability.

Thus, the event in this case will be the probability of drawing a ball. Here it is given that there are balls that are numbered from 10 to 24. Thus, this will be our total set. Thus set S is given as:

S={ 10, 11, 12, 13, 14, 15, 16, 17, 18 ,19, 20, 21, 22, 23, 24 }

Since each ball is numbered with one number between 10 and 24 we can say that the total number of balls that are present is 15.

It is said that a single ball is drawn at random from this set of 15 balls.

(i) The probability of drawing the ball numbered 23 is asked to be found out. Since the ball is picked at random and since there is only a single ball that is numbered 23 the probability will be:

$P(A)=\frac{1}{15}$

This means that there is only one favourable outcome of picking a single ball out of 15 balls.

(ii) The probability of drawing the ball numbered with an odd number is asked to be found out.

We know that an odd number is a number that is not divisible or is not a multiple of 2. Thus, if we look at the set S the count of odd numbers between 10 to 24 will be 7. The probability will be

$P(A)=\frac{7}{15}$

This is because there are 7 balls so 7 possibilities which means that any of these 7 balls can be picked out of a total of 15 balls.

(iii) A composite number is a number which is not prime. This means that it consists of two or more factors other than 1 and itself. They are numbers which have smaller numbers that can be multiplied to produce this number.

Since we have 10 non-prime numbered balls namely 10, 12,14,15,16,18,20,21,22,24; the probability will be:

$P(A)=\frac{10}{15}$

(iv) Perfect squares are numbers which when taken the square root of gives a whole number. This means that when a number is squared it gives a number which is a perfect square.

From set S it can be seen that there is only one number that is a perfect square which is the number 16.

Hence the ball numbered 16 is the only possibility to be picked at random out of 15 balls and hence the probability will be:

$P(A)=\frac{1}{15}$

(v) Similar to a perfect square a perfect cube is a number which when taken the cubic root of gives a whole number. A number multiplied with itself for 3 times results in a number which is a perfect cube.

Thus, from the set S it can be observed that there are no perfect cubes which means that there is no possibility of occurrence of the event so the probability will be zero.

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