Question

a) P(heads, then P)b) P(tails, then a vowel)2. A coin is tossed, then aletter from the wordINDIANAPOLIS is selected atrandom. Find eachprobability.c) P(tails, then N)d) P(heads, then D or 1)

Answer 1

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:

`P(head\text{ and P\rparen= }P(heads)* P(P)`

The probability of getting heads is 1 out of 2 since there are only two possible outcomes, therefore, we have:

`P(heads)=(1)/(2)`

The probability of getting "P" is equivalent to the quotient between the number of "P's" and the total number of letters:

`P(P)=(1)/(12)`

Now, we substitute in the product:

`P(heads\text{ and P\rparen=}(1)/(2)*(1)/(12)`

Solving the product:

`P(heads\text{ and P\rparen=}(1)/(24)`

Therefore, the probability is 1/24.

The same procedure is used to determine the other probabilities.