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Question
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 a one-digit number,
Solution
Given number 6, 7, 8, .... , 70 form an AP with a = 6 and d = 1.
Let Tn = 70. Then,
6 + (n − 1)1 = 70
⇒ 6 + n − 1 = 70
⇒ n = 65
Thus, total number of outcomes = 65.
(i) Let E1 be the event of getting a one-digit number.
Out of these numbers, one-digit numbers are 6, 7, 8 and 9.
Number of favourable outcomes = 4.
∴ P(getting a one-digit number) = P(E1) = `("Number of outcomes favourable to" E_2)/"Number of all possible outcomes"`
`= 4/65`
Thus, the probability that the card bears a one-digit number is `4/65`.
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