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A letter is chosen at random from the letters of the word PROBABILITY. Find the probability that letter chosen is a vowel
- a)1/30
- b)4/11
- c)1/6
- d)1/5
- e)1/3
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A letter is chosen at random from the letters of the wordPROBABILITY. ...
On the first pick, two of the five letters are vowels — A & E — so the probability of picking a vowel on the first pick is 2/5. On the second pick, only one letter out of the six is a vowel — O — so the probability of picking a vowel on the second pick is 1/6. The two picks are independent: what one selects from one set has absolutely no bearing on what one picks from the other set. Therefore, we can use the generalized AND rule.
P(two vowels) = P(vowel on first pick)*P(vowel on second pick) = (2/5)*(1/6) = 2/30 = 1/15
Most Upvoted Answer
A letter is chosen at random from the letters of the wordPROBABILITY. ...
Probability of Picking Two Vowels
To determine the probability of picking two vowels, we need to understand the total number of possibilities and the number of favorable outcomes.
Total Number of Possibilities:
To calculate the total number of possibilities, we need to know the total number of choices available. In this case, we assume that we are picking from a set of 30 alphabets.
Number of Favorable Outcomes:
To find the number of favorable outcomes, we need to determine the number of vowels in the set of alphabets. Vowels are the letters 'A', 'E', 'I', 'O', and 'U'. In this case, we assume that there are 5 vowels in the set.
Calculating the Probability:
The probability of picking two vowels can be calculated using the formula:
Probability = Number of Favorable Outcomes / Total Number of Possibilities
Let's calculate the probability using the given values:
Number of Favorable Outcomes = 5 (as there are 5 vowels in the set)
Total Number of Possibilities = 30 (as there are 30 alphabets in the set)
Probability = 5 / 30 = 1/6
Therefore, the correct answer is option C) 1/6.
Explanation:
The probability of picking two vowels is 1/6. This means that out of all the possible choices, there is a 1 in 6 chance of picking two vowels. This can be understood by considering all the possible combinations of two alphabets from the set of 30. Since there are 5 vowels in the set, there are 5 choices for the first vowel and 4 choices for the second vowel. The total number of combinations is obtained by multiplying these choices together: 5 * 4 = 20. However, this counts each combination twice (e.g., picking 'A' then 'E' is the same as picking 'E' then 'A'), so we need to divide by 2 to get the correct number of combinations: 20 / 2 = 10. Finally, we divide the number of favorable outcomes (10) by the total number of possibilities (30) to obtain the probability: 10 / 30 = 1/6.
To determine the probability of picking two vowels, we need to understand the total number of possibilities and the number of favorable outcomes.
Total Number of Possibilities:
To calculate the total number of possibilities, we need to know the total number of choices available. In this case, we assume that we are picking from a set of 30 alphabets.
Number of Favorable Outcomes:
To find the number of favorable outcomes, we need to determine the number of vowels in the set of alphabets. Vowels are the letters 'A', 'E', 'I', 'O', and 'U'. In this case, we assume that there are 5 vowels in the set.
Calculating the Probability:
The probability of picking two vowels can be calculated using the formula:
Probability = Number of Favorable Outcomes / Total Number of Possibilities
Let's calculate the probability using the given values:
Number of Favorable Outcomes = 5 (as there are 5 vowels in the set)
Total Number of Possibilities = 30 (as there are 30 alphabets in the set)
Probability = 5 / 30 = 1/6
Therefore, the correct answer is option C) 1/6.
Explanation:
The probability of picking two vowels is 1/6. This means that out of all the possible choices, there is a 1 in 6 chance of picking two vowels. This can be understood by considering all the possible combinations of two alphabets from the set of 30. Since there are 5 vowels in the set, there are 5 choices for the first vowel and 4 choices for the second vowel. The total number of combinations is obtained by multiplying these choices together: 5 * 4 = 20. However, this counts each combination twice (e.g., picking 'A' then 'E' is the same as picking 'E' then 'A'), so we need to divide by 2 to get the correct number of combinations: 20 / 2 = 10. Finally, we divide the number of favorable outcomes (10) by the total number of possibilities (30) to obtain the probability: 10 / 30 = 1/6.
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