# A Box Contains Cards Bearing Numbers 6 to 70. If One Card is Drawn at Random from the Box, Find the Probability that It Bears an Odd Number Less than 30. - Mathematics

Short Note

A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box, find the probability that it bears an odd number less than 30.

#### Solution

Let E3 be the event of getting an odd number less than 30.

Out of these numbers, odd numbers less than 30 are 7, 9, 11, ... , 29.
Given number 7, 9, 11, .... , 29 form an AP with a = 7 and d = 2.
Let Tn = 29. Then,
7 + (n − 1)2 = 29
⇒ 7 + 2n  − 2 = 29
⇒ 2n = 24
⇒ n = 12

Thus, number of favourable outcomes = 12.

∴ P(getting an odd number less than 30) = P(E3) = ("Number of outcomes favourable to"  E_3)/"Number of all possible outcomes"

Thus, the probability that the card bears an odd number less than 30 is 12/65.

Concept: Concept Or Properties of Probability
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 15 Probability
Exercise 15B | Q 5.3 | Page 696