Final answer:
The probability of selecting a 'B' followed by an 'O' without replacement from the word OCTOBER is found by multiplying the individual probabilities of each event: 1/7 for the 'B' and 1/3 for the 'O', resulting in a combined probability of 1/21. The correct answer is option H.
Step-by-step explanation:
The student is asking for the probability of selecting a 'B' and then an 'O' from the letters of the word OCTOBER without replacement. To solve this, we need to calculate the probabilities of each event happening one after the other. Initially, the bag contains 7 letters, so the probability of picking a 'B' is 1/7 (since there is only one 'B' in OCTOBER).
Once the 'B' is picked, it is not replaced, meaning there are now 6 letters left in the bag. Among them, there are 2 'O's, so the probability of then picking an 'O' is 2/6, which simplifies to 1/3.
The combined probability of both events happening in sequence is found by multiplying their individual probabilities together: (1/7) * (1/3), which equals 1/21.
The correct answer is H. 1/21