Cora is playing a game that involves flipping three coins at once.
Let the random variable \[H\] be the number of coins that land showing "heads". Here is the probability distribution for \[H\]:
\[H= \# \text{ of heads}\]	\[0\]	\[1\]	\[2\]	\[3\]
\[P(H)\]	\[0.125\]	\[0.375\]	\[0.375\]	\[0.125\]
\[P(H < 3)=\] 


We are given the probability distribution for the random variable \( H \), representing the number of heads when flipping three coins. The table shows the values of \( H \) and the corresponding probabilities:

\[
\begin{array}{|c|c|}
\hline
H = \# \text{ of heads} & P(H) \\
\hline
0 & 0.125 \\
1 & 0.375 \\
2 & 0.375 \\
3 & 0.125 \\
\hline
\end{array}
\]

To find \( P(H < 3) \), we sum the probabilities for \( H = 0 \), \( H = 1 \), and \( H = 2 \), since these are all the cases where the number of heads is less than 3:

\[
P(H < 3) = P(H = 0) + P(H = 1) + P(H = 2)
\]

Substitute the values from the table:

\[
P(H < 3) = 0.125 + 0.375 + 0.375 = 0.875
\]

Thus, the probability that the number of heads is less than 3 is \( P(H < 3) = 0.875 \).

Would you like more details on probability distributions or the method used here?

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Here are 5 related questions for further exploration:
1. What is \( P(H \geq 2) \) based on the distribution?
2. How would you compute the expected value of \( H \)?
3. What is the probability of getting exactly one head, \( P(H = 1) \)?
4. How would the distribution change if the game used four coins instead of three?
5. What is the variance of \( H \) for this probability distribution?

**Tip:** When summing probabilities, always ensure they add up to 1 to verify the distribution is valid.

Cora is playing a game that involves flipping three coins at once. Let the random variable \[H\] be the number of coins that land showing 'heads'. Here is the probability distribution for \[H\]: \[H= \# \text{ of heads}\] \[0\] \[1\] \[2\] \[3\] \[P(H)\] \[0.125\] \[0.375\] \[0.375\] \[0.125\] \[P(H < 3)=\]

Explore the probability distribution for flipping three coins, focusing on the random variable \[H\] representing the number of heads. Understand how to calculate \[P(H < 3)\] using the provided probability distribution table. Suitable for students in Grades 10-12.

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