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Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has an even number

Solution:

Given, cards with numbers 2 to 101 are placed in a box.

A card is selected at random.

We have to find the probability that the card has an even number.

Total number cards = 100

Using arithmetic progression to find the number of cards with even numbers.

The last term is given by l = a + (n - 1)d

Where, l is the last term

a is the first term

n is the number of terms

d is the common difference

Given, cards with numbers 2 to 101. We need a total number of even numbers in the given cards.

a = 2

l = 100

d = 2

So, 100 = 2 + (n - 1)2

100 - 2 = 2n - 2

100 - 2 + 2 = 2n

100 = 2n

n = 100/2

n = 50

Number of favourable outcomes = 50

Number of possible outcomes = 100

Probability = number of favoruable outcomes / number of possible outcomes

Probability = 50/100

= 5/10

= 1/2

Therefore, the probability of selecting a card that has an even number is 1/2.

✦ Try This: Cards with numbers 102 to 201 are placed in a box. A card is selected at random. Find the probability that the card has an odd number.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14

NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 32(i)

Cards with numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has an even number

Summary:

Cards with numbers 2 to 101 are placed in a box. A card is selected at random. The probability that the card has an even number is 1/2

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