Question

A box contains cards numbered from 15 to 130. A card is drawn at random from the box.

Find the probability that the number on the card drawn is ;

a) a perfect square number ; b) a multiple of 5.​

Answer 1

Probability it is a perfect square is 1/9

Step-by-step explanation:

{S}={6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26...50}

n{S}=45

{A}={9,16,25,36,49}

n{A}={5}

{P}= n{A}/n{S}

= 5/45

= 1/9

Answer 2

Given:

• A box contains cards numbered from 15 to 130. A card is drawn at random from the box.

To find:

• Probability that the number of cards drawn is,

1. A perfect square number
2. A multiple of 5.

Solution:

Given no. of cards = 15,16,17,18,19,20,......,130

Total no. of cards = 130 - 15 + 1 = 116

1) Probability that the number of cards drawn is a perfect square number.

Therefore,

We know that, square of numbers,

→ 1², 2², 3², 4², 5², 6², 7², 8², 9², 10², 11², 12²,..........

= 2, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144,......

Square no. between 15 to 130 are 16,25,36,79,64,81,100,121

So, number of square numbers between 15 to 130 is 8.

We know that,

★ P(E) = Total no. of possible outcome/Total no. of outcomes

Here,

• Total no. of outcome = No. of cards = 116

• Total number of possible outcomes = number of square numbers between 15 to 123 = 8

Therefore, Probability of getting a square no. = 8/116 = 0.068

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2) Probability that the number of cards drawn is a multiple of 5.

We know that,

Multiple of 5 are,

→ 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95,......

So, the number of multiples of 5 between 15 to 130 is 24.

Here,

• Total no. of outcome = No. of cards = 116

• Total number of possible outcomes = number of multiples of 5 between 15 to 130 = 24

Thus, The probability of getting a multiple of 5 = 24/116 = 0.206