Final answer:
The probability of picking a letter B from the word "basketball" is 1/5, and then the probability of picking a vowel from the remaining letters is 5/9. To find the combined probability of both events, we multiply these probabilities to get 1/9.
Step-by-step explanation:
The student has asked about the probability of choosing a specific letter from a bag and then choosing a vowel, given that the letters are from the word basketball. To calculate this, we need to consider two successive probabilities.
The probability of choosing a B first is determined by the number of B's in the word basketball divided by the total number of letters in the word. There are 2 B's in the word basketball, which has 10 letters in total. So, the probability of picking a B first is 2/10 or 1/5.
After removing a B, there are 9 letters left. The probability of choosing a vowel next would be the number of vowels remaining divided by the new total number of letters. In basketball without the letter B, there are 3 A's and 2 E's, which makes for 5 vowels out of 9 letters total. So, the probability of picking a vowel after removing a B is 5/9.
To find the combined probability of both events happening, we multiply the two probabilities together: (1/5) × (5/9) = 1/9. Therefore, the probability of picking a B followed by a vowel from the word basketball without replacement is 1/9.