A letter is chosen at random from the letters in the word PROBABILITY . What is the probability that tha letter will be B or vowel ?

Answer

To solve the problem of finding the probability that a letter chosen at random from the word "PROBABILITY" will be either 'B' or a vowel, we can follow these steps:

### Step 1: Identify the total number of letters in the word "PROBABILITY".
The word "PROBABILITY" consists of the following letters: P, R, O, B, A, B, I, L, I, T, Y.

**Total letters = 11**

### Step 2: Identify the vowels in the word.
The vowels in the English language are A, E, I, O, U. In the word "PROBABILITY", the vowels present are:
- A
- I
- O

Counting these, we find:
- A: 1
- I: 2
- O: 1

**Total number of vowels = 1 (A) + 2 (I) + 1 (O) = 4**

### Step 3: Count the occurrences of the letter 'B'.
In the word "PROBABILITY", the letter 'B' appears twice.

**Total number of B's = 2**

### Step 4: Calculate the total number of favorable outcomes.
We need to find the total number of favorable outcomes, which includes the number of vowels and the occurrences of 'B'. However, we must be careful not to double count the 'B's since they are not vowels.

- Number of vowels = 4
- Number of B's = 2

Since 'B' is not a vowel, we can simply add these two counts together:
**Total favorable outcomes = Number of vowels + Number of B's = 4 + 2 = 6**

### Step 5: Calculate the probability.
The probability of an event is given by the formula:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we have:

\[ \text{Probability} = \frac{6}{11} \]

### Final Answer:
The probability that the letter chosen will be 'B' or a vowel is \(\frac{6}{11}\).

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