lesson 3: sample spaces\ncool down: sample space of sample space\none letter is chosen at random from the…

lesson 3: sample spaces\ncool down: sample space of sample space\none letter is chosen at random from the word sample then a letter is chosen at random from the word space.\n1. write all of the outcomes in the sample space of this chance experiment.\n2. how many outcomes are in the sample space?\n3. what is the probability that the letters chosen are aa? explain your reasoning.

lesson 3: sample spaces\ncool down: sample space of sample space\none letter is chosen at random from the word sample then a letter is chosen at random from the word space.\n1. write all of the outcomes in the sample space of this chance experiment.\n2. how many outcomes are in the sample space?\n3. what is the probability that the letters chosen are aa? explain your reasoning.

Answer

Explanation:

Step1: List all outcomes

The word "SAMPLE" has 6 letters and the word "SPACE" has 5 letters. We pair each letter from "SAMPLE" with each letter from "SPACE". The sample - space outcomes are: SA, SP, SC, SA, SE, PA, PP, PC, PA, PE, MA, MP, MC, MA, ME, LA, LP, LC, LA, LE, EA, EP, EC, EA, EE.

Step2: Count the number of outcomes

The number of outcomes in the sample space is the product of the number of letters in "SAMPLE" and the number of letters in "SPACE". Since there are 6 letters in "SAMPLE" and 5 letters in "SPACE", the number of outcomes $n = 6\times5=30$.

Step3: Calculate the probability of getting 'AA'

There is only 1 way to get 'AA' out of 30 possible outcomes. The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So the probability of getting 'AA' is $P=\frac{1}{30}$.

Answer:

  1. SA, SP, SC, SA, SE, PA, PP, PC, PA, PE, MA, MP, MC, MA, ME, LA, LP, LC, LA, LE, EA, EP, EC, EA, EE
  2. 30
  3. $\frac{1}{30}$, because there is 1 favorable outcome (getting 'AA') out of 30 total possible outcomes.