we are asked to determine the probability of getting heads and the letter "P" from the word "INDIANAPOLIS". To do that we will use the product rule of probabilities:
[tex]P(head\text{ and P\rparen= }P(heads)\times P(P)[/tex]
The probability of getting heads is 1 out of 2 since there are only two possible outcomes, therefore, we have:
[tex]P(heads)=\frac{1}{2}[/tex]
The probability of getting "P" is equivalent to the quotient between the number of "P's" and the total number of letters:
[tex]P(P)=\frac{1}{12}[/tex]
Now, we substitute in the product:
[tex]P(heads\text{ and P\rparen=}\frac{1}{2}\times\frac{1}{12}[/tex]
Solving the product:
[tex]P(heads\text{ and P\rparen=}\frac{1}{24}[/tex]
Therefore, the probability is 1/24.
The same procedure is used to determine the other probabilities.
