There are 20 women in a bus, 15 of them wear glasses and 10 wear wrist watches. If a woman is chosen at random from the bus, find the probability that she wears both glasses and wrist watch.
if x wear both,
15+10-x = 20
x = 5
so P(both) = 5/20
Well, if we consider the 20 women on the bus, let's say they're all part of a secret society called "Glasses and Watches enthusiasts." Out of these 20 women, 15 wear glasses and 10 wear wristwatches. So, some of them might be Glasses enthusiasts, some might be Watch enthusiasts, and there could be a special group of women who are truly dedicated and are both Glasses and Watches enthusiasts.
To find the probability that a woman wears both glasses and a wristwatch, we need to count how many women fall into this special group. If there's no overlap between these two groups, then there could only be 10 women who are truly dedicated and wear both glasses and watches.
So, the probability would be 10 out of 20, or 10/20, which simplifies to 1/2. Therefore, the probability of randomly choosing a woman who wears both glasses and a wristwatch is half, just like having a 50-50 chance of being fantastic or fabulous.
To find the probability that a woman wears both glasses and a wristwatch, we need to determine the number of women who wear both glasses and a wristwatch and divide it by the total number of women in the bus.
Given information:
Total number of women = 20
Number of women wearing glasses = 15
Number of women wearing wristwatches = 10
To calculate the probability, we need to find the number of women who wear both glasses and a wristwatch.
Let's start by finding the maximum number of women that could wear both glasses and a wristwatch. Since there are only 10 women wearing wristwatches, the maximum number of women wearing both is 10.
However, the number of women wearing glasses is 15, which exceeds the maximum limit of 10 women. Therefore, we can conclude that the maximum number of women wearing both glasses and wristwatches is 10.
So, the number of women wearing both glasses and a wristwatch is 10.
To find the probability, we divide the number of women wearing both glasses and a wristwatch by the total number of women in the bus.
Probability = Number of women wearing both glasses and wristwatch / Total number of women
Probability = 10 / 20
Simplifying the fraction,
Probability = 1/2
Therefore, the probability that a woman chosen at random from the bus wears both glasses and a wristwatch is 1/2.
To find the probability that a woman chosen randomly from the bus wears both glasses and a wristwatch, we need to determine two things:
1. The number of women who wear both glasses and wristwatches.
2. The total number of women on the bus.
First, let's calculate the number of women who wear both glasses and wristwatches. We can do this by taking the smaller value between the number of women wearing glasses (15) and the number of women wearing wristwatches (10). In this case, the smaller value is 10, so we can conclude that there are 10 women who wear both glasses and wristwatches.
Next, let's determine the total number of women on the bus, which is given as 20.
Now that we have both pieces of information, we can compute the probability. The probability of an event occurring is defined as:
Probability = Number of Successful Outcomes / Total Number of Possible Outcomes
In this case, the "successful outcome" is a woman who wears both glasses and a wristwatch, which we determined to be 10. The "total possible outcomes" represent the total number of women on the bus, which is given as 20.
Therefore, the probability that a woman chosen at random from the bus wears both glasses and a wristwatch is:
Probability = 10 / 20 = 0.5
So, the probability is 0.5 or, in percentage form, 50%.