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Chapter 35: Problem 1121

From 20 tickets marked with the first 20 numerals, one is drawn at random: find the chance that it is a multiple of 3 or of 7 .

Short Answer

Expert verified
The probability of drawing a ticket which is a multiple of 3 or 7 from 20 tickets marked with the first 20 numerals is \(0.4\).

Step by step solution

01

Identify the multiples of 3 and 7

We need to find ticket numbers that are divisible by 3 or 7 among the 20 tickets. Let's list them down: Multiples of 3: 3, 6, 9, 12, 15, 18 Multiples of 7: 7, 14
02

Count the number of multiples

Now we have identified the ticket numbers that are multiples of 3 or 7, let's count them. Total number of multiples of 3 among 20 tickets: 6 (3, 6, 9, 12, 15, 18) Total number of multiples of 7 among 20 tickets: 2 (7, 14) Total number of multiples of 3 or 7 among 20 tickets = 6 + 2 = 8. However, we need to check if any multiple is repeated in both the sets. In our case, there is no common multiple of 3 and 7 in the range of 1 to 20.
03

Calculate the probability

Now, let's calculate the probability of drawing a ticket which is a multiple of 3 or 7. To find the probability, we have to divide the count of such favorable outcomes by the total number of possible outcomes. Total number of favorable outcomes (tickets that are multiples of 3 or 7) = 8 Total number of possible outcomes (total number of tickets) = 20 Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 8 / 20 = 0.4 The probability of drawing a ticket which is a multiple of 3 or 7 is 0.4.

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