Lottery Probability: Meena calculates that the probability of her winning the first prize in a lottery is…

Lottery Probability: Finding the Number of Tickets Bought

Imagine you are holding a lottery ticket, waiting for the drawing. What are your actual chances of winning? To answer that, we have to look at the core idea of probability. At its heart, probability is just a simple fraction that measures chance.

We build this fraction using two simple numbers. On top, we place our favorable outcomes—the specific results we are hoping to see. On the bottom, we divide by the total possible outcomes—every single thing that could happen. Let's look at how this looks visually.

So, if there is exactly one winning ticket out of four total tickets in our pool, the math is straightforward. The probability of picking that winning ticket is one over four, which is a twenty-five percent chance.

To find how many tickets Meena bought, let's first visualize her share of the entire lottery pool. Imagine this large outer box represents all the tickets sold in the lottery.

Now, Meena holds a small slice of this pool. We are told her probability of winning is exactly zero point zero eight. That is the same as eight percent, or eight out of every one hundred tickets.

This visual makes the relationship clear: the ratio of Meena's tickets to the total tickets is exactly equal to her probability of winning. Next, we will use this ratio to calculate the total number of tickets in play.

Now that we understand Meena's share of the lottery, let's translate this word problem into a clean algebraic equation. Remember our core formula: the probability of an event is simply the number of favorable outcomes divided by the total possible outcomes.

Let's substitute what we know from the problem. The probability of winning is given as zero point zero eight. The total number of tickets sold is six thousand. We don't know how many tickets Meena bought, so we will represent that unknown value with the variable x.

Putting it all together, we get a beautiful, simple mathematical proportion: zero point zero eight equals x divided by six thousand. This equation is our bridge, ready to be solved to find the exact number of tickets.

Now, let's solve our equation to find exactly how many tickets Meena bought. To isolate x, we multiply both sides of our equation by fifteen million.

Before doing any heavy division, let's simplify this fraction by canceling out the matching zeros at the end of both numbers. We can cross out four zeros from the top and four zeros from the bottom.

Now we are left with fifteen hundred divided by twenty-five. Think of twenty-five as a quarter. Since four quarters make one hundred, fifteen hundreds must contain fifteen times four, which is exactly sixty.