# Probablity of choosing the same number

In summary, the probability of choosing the same number twice in a row depends on the total number of options available and whether the selection is made with or without replacement. As the number of options increases, the probability decreases. With replacement, the probability remains the same for each selection, but without replacement, it decreases with each selection. The probability cannot be higher than 100% as it is a measure of likelihood. The probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
There's a problem... What is the probabilty that 4 people would choose the same number from 1 to 4? (e.g they all choose 2)...i think it should be like (4/4*1/4*1/4*1/4=1/64) ...just want to double check cause this is an importatnt quesiton...thanks

Yup. (1/4)^4 for all the same of a given number * 4 for the four numbers.

thanks a lot...

## 1. What is the probability of choosing the same number twice in a row?

The probability of choosing the same number twice in a row depends on the total number of options available and whether the selection is made with replacement or without replacement. For example, if you are choosing from a deck of cards with replacement, the probability would be 1/52 or approximately 1.92%. If you are choosing without replacement, the probability would be 1/13 or approximately 7.69%.

## 2. Does the probability of choosing the same number change if there are more options available?

Yes, the probability of choosing the same number changes as the number of options available increases. This is because the total number of possible outcomes increases, making it less likely to choose the same number twice in a row. For example, if you are choosing from a deck of cards with 52 options, the probability would be 1/52. But if you are choosing from a deck of cards with 104 options, the probability would decrease to 1/104.

## 3. How does the probability of choosing the same number change if the selection is made with or without replacement?

The probability of choosing the same number changes depending on whether the selection is made with or without replacement. With replacement, the probability remains the same for each selection. For example, if you are choosing from a deck of cards with replacement, the probability would be 1/52 for each selection. Without replacement, the probability changes with each selection as the number of options decreases. For example, if you are choosing from a deck of cards without replacement, the probability would be 1/52 for the first selection, but only 1/51 for the second selection.

## 4. Can the probability of choosing the same number be higher than 100%?

No, the probability of choosing the same number cannot be higher than 100%. This is because probability is a measure of the likelihood of an event occurring, ranging from 0% to 100%. Therefore, the probability of choosing the same number twice in a row can never be higher than 100%, as it is a single event with a finite number of options.

## 5. How can I calculate the probability of choosing the same number?

The probability of choosing the same number can be calculated by dividing the number of favorable outcomes (choosing the same number) by the total number of possible outcomes. For example, if you are choosing from a deck of cards, there is only one favorable outcome (choosing the same card), and 52 possible outcomes. Therefore, the probability would be 1/52 or approximately 1.92%. This formula can be applied to any situation where the number of favorable outcomes and total number of outcomes are known.

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