This is a question about compound events:
The game of Scrabble includes 100 lettered tiles. 42 of the tiles represent vowels. If you select a tile, put it back, and select again, what is the probability of getting a vowel both times?
The probability of getting both (or all) events is obtained by multiplying the probability of the individual events.
The probability of getting a vowel one time is 42/100 = .42
I hope this helps. Thanks for asking.
To find the probability of getting a vowel both times, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
Since you select a tile, put it back, and then select again, you have two independent selections. For each selection, you have a total of 100 possible tiles to choose from. Therefore, the total number of outcomes for both selections is 100 * 100 = 10,000.
Number of Favorable Outcomes:
The number of vowels in the game is given as 42. Since you put the tile back after each selection, the number of vowels remains the same for the second selection. Therefore, the number of favorable outcomes for both selections is 42 * 42 = 1,764.
Probability Calculation:
Probability is the ratio of favorable outcomes to total outcomes. So, the probability of getting a vowel twice can be calculated as:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
Probability = 1,764 / 10,000
Simplifying this fraction, we get:
Probability = 0.1764
Therefore, the probability of getting a vowel both times is approximately 0.1764, or 17.64%.