A box contains 90 discs which are numbered from 1 to 90 . If one disc is drawn at random from the box ' find the probability that it bears (1) a two_ digit number (2) a number divisible by 5 Related: Probability Problem Solving?

Question

A box contains 90 discs which are numbered from 1 to 90 . If one disc is drawn at random from the box ' find the probability that it bears                       (1) a two_ digit number                               (2) a number divisible by 5 Related:  Probability Problem Solving?

Answer

1) There are 90 numbers from 1 to 90 out of which numbers from 1 to 9 are the only single digit numbers and the rest 81 are two digit numbers.

So, probability of getting a two digit number = 81/90 = 9/10 = 0.9

2) The numbers which are divisible by 5 from 1 to 90 are,

{5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90}

So, probability of getting a multiple of 5 = 18/90 = 2/10 = 0.2

Another way to do without counting is that, if you divide all the numbers into sets of 10 numbers starting from 1 (like 1-10, 11-20, 21-30,etc) each set will have two multiples of 5. So, the probability will be 2/10 = 0.2

Answer

Answer

**Probability of drawing a two-digit number:**

To find the probability of drawing a two-digit number, we need to determine the number of favorable outcomes (two-digit numbers) and the total number of possible outcomes (all numbers from 1 to 90).

1. Determine the number of favorable outcomes:
- Two-digit numbers range from 10 to 99.
- The total number of two-digit numbers can be found by subtracting the number of one-digit numbers (1 to 9) from the total number of numbers from 1 to 99.
- The number of one-digit numbers is 9 (as there are nine digits from 1 to 9).
- Therefore, the number of two-digit numbers is 99 - 9 = 90.

2. Determine the total number of possible outcomes:
- The total number of possible outcomes is the total number of numbers from 1 to 90, which is 90.

3. Calculate the probability:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- In this case, the probability of drawing a two-digit number is 90 (number of favorable outcomes) divided by 90 (total number of possible outcomes).
- Therefore, the probability is 90/90 = 1.

**Probability of drawing a number divisible by 5:**

To find the probability of drawing a number divisible by 5, we need to determine the number of favorable outcomes (numbers divisible by 5) and the total number of possible outcomes (all numbers from 1 to 90).

1. Determine the number of favorable outcomes:
- Numbers divisible by 5 have a remainder of 0 when divided by 5.
- The first number divisible by 5 is 5, and the last number divisible by 5 is 90.
- To find the number of numbers divisible by 5, we can divide 90 by 5 and round down to the nearest whole number.
- The number of numbers divisible by 5 is floor(90/5) = floor(18) = 18.

2. Determine the total number of possible outcomes:
- The total number of possible outcomes is the total number of numbers from 1 to 90, which is 90.

3. Calculate the probability:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- In this case, the probability of drawing a number divisible by 5 is 18 (number of favorable outcomes) divided by 90 (total number of possible outcomes).
- Therefore, the probability is 18/90 = 1/5 = 0.2.

In summary, the probability of drawing a two-digit number from the box is 1, and the probability of drawing a number divisible by 5 is 0.2.

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