# How many handshakes occur at a party with 16 people?

• ParisSpart
In summary, 16 people can be paired in 8 ways. If you choose 2 people from 16, you can choose the first in 16 ways and the second in 15 ways.
ParisSpart
16 people Meet together at a party. Each pair of these individuals decide to chance whether you hailed by handshake or not (probability handshake = 0.40). On average, how many handshakes occur?

X=handshakes if 1 and no handshakes if 0
X=X1+X2+X3+X4+X5+X6+X7+X8 and E(X)=E(X1)+...+E(X8)=8*0.40 but its says tha its not correct where is wrong?

ParisSpart said:
16 people Meet together at a party. Each pair of these individuals decide to chance whether you hailed by handshake or not (probability handshake = 0.40). On average, how many handshakes occur?

X=handshakes if 1 and no handshakes if 0
X=X1+X2+X3+X4+X5+X6+X7+X8 and E(X)=E(X1)+...+E(X8)=8*0.40 but its says tha its not correct where is wrong?

You say that 16 people can be paired in only 8 ways?

256?

ParisSpart said:
256?

Work it out. Don't guess!

each person can be paired with other 15 people so we have 15*16=240 but 240*0.40 its not correct where is my wrong?

the way thst i solve this is wrong?

ParisSpart said:
each person can be paired with other 15 people so we have 15*16=240 but 240*0.40 its not correct where is my wrong?

this means that you cannot help?

ParisSpart said:
each person can be paired with other 15 people so we have 15*16=240 but 240*0.40 its not correct where is my wrong?
If you choose 2 people from 16, you can choose the first in 16 ways and the second in 15 ways. But for a given pair, you don't care what order you chose them in. Try it with smaller numbers, like 2 from 2, 2 from 3...

If you honestly have no idea how to even approach this problem, where did you get it? If this really is homework, clearly your teacher expects you to know things that you apparently don't. You really need to talk to your teacher about this.

## 1. What is the definition of probability expected value?

The probability expected value is a mathematical concept that represents the average value of a random variable over a large number of trials. It takes into account both the likelihood of different outcomes and the values associated with those outcomes.

## 2. How is the probability expected value calculated?

The probability expected value is calculated by multiplying each possible outcome by its corresponding probability and then summing all of these products. This can also be represented by the formula: E(X) = Σ x * P(x), where x is the possible outcome and P(x) is the probability of that outcome.

## 3. What is the significance of the probability expected value?

The probability expected value is a useful tool for decision making and risk assessment. It allows us to understand the average outcome of a situation and make informed decisions based on this knowledge.

## 4. Can the probability expected value be negative?

Yes, the probability expected value can be negative. This means that the expected outcome is likely to result in a loss or a decrease in value. However, it is important to consider other factors such as the potential gains and the associated risks before making any decisions.

## 5. How does the concept of probability expected value relate to real-world scenarios?

The concept of probability expected value is applicable in various real-world scenarios, such as business, finance, and insurance. For example, a company may use this concept to determine the expected return on a new investment, or an insurance company may use it to calculate the expected losses from a particular policy. It can also be used in gambling to assess the potential outcomes and make informed decisions.

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