Numbers 1 to 50 are written on 50 separate cards (one number on one card), kept in a box
and mixed well. One card is drawn at random from the box. Find the probability of getting
(i) a one-digit number.
(ii) a number greater than 25.
Explain with diagram and images or figure if possible in the video and write all step by step solution of each question in simplest way for class 8 child
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Let's solve a probability problem about drawing cards. We have 50 cards numbered from 1 to 50 in a box. We need to find the probability of drawing a one-digit number and the probability of drawing a number greater than 25. First, let's understand what we have: 50 cards with numbers 1 through 50, and we draw one card randomly.
Before solving the problem, let's understand the probability formula. Probability equals the number of favorable outcomes divided by the total number of possible outcomes. In our case, we have 50 total cards, so the total number of outcomes is 50. The favorable outcomes depend on what we're looking for - either one-digit numbers or numbers greater than 25.
Let's solve part i: finding the probability of getting a one-digit number. First, we identify the one-digit numbers from 1 to 50. These are 1, 2, 3, 4, 5, 6, 7, 8, and 9. That's 9 numbers in total. Using our probability formula, the probability equals 9 favorable outcomes divided by 50 total outcomes, which gives us 9 over 50.
Now let's solve part ii: finding the probability of getting a number greater than 25. The numbers greater than 25 are 26, 27, 28, and so on up to 50. To count these, we can think: from 1 to 25 there are 25 numbers, so from 26 to 50 there must be 50 minus 25, which equals 25 numbers. Using our probability formula, we get 25 over 50, which simplifies to 1 over 2 or one half.
Let's summarize our complete solution. For part i, the probability of getting a one-digit number is 9 over 50. For part ii, the probability of getting a number greater than 25 is 25 over 50, which simplifies to 1 over 2. Remember the key steps: identify favorable outcomes, count total outcomes, apply the probability formula, and simplify when possible. These fundamental probability concepts will help you solve many similar problems.