Final answer:
The probability calculation yields a result of 1/2. The question involves finding the probability of picking an even-numbered ball from a box after a transfer from another box. Option E.
Step-by-step explanation:
The question involves calculating the probability of Lily picking an even-numbered ball from box 2 after Jill moves one ball from box 1 to box 2.
To find the probability, we consider all possible outcomes in which an even-numbered ball is picked from box 2.
Since box 1 has two even-numbered balls (6 and 8) and one odd (7), there's a 2/3 chance that an even-numbered ball is transferred to box 2.
Initially, box 2 has two even (0 and 2) and one odd (1), making three even-numbered balls once an even-numbered ball is moved from box 1 to box 2.
Hence, Lily has a 3/4 chance of picking an even number.
As a whole, the probability that Lily picks an even number is the product of these two independent probabilities:
- Probability Jill picks an even number from box 1: 2/3
- Probability Lily picks an even number from box 2 after the transfer: 3/4
Multiplying these probabilities gives:
2/3 * 3/4 = 1/2
Hence, the right answer is option E. 1/2
The complete question is:
There are two boxes each contain 3 number balls. box 1 has number 6,7 and 8. box 2 has 0,1 and 2. jill picks one ball from box 1 and places it in box 2. then lily pick one ball from box 2 without looking. what is the probability that lily will pick a ball with even number? a. 1/16 b. 4/9 c. 9/32 d. 2/9 e. 1/2