Need some help please!

A box contains four good light bulbs and three defective ones. Bulbs are selected one at a time (without replacement). Find the probability that the second defective bulb is found on the third selection.

let g be good bulb

let b be bad bulb
so your events are:
gbb ---> (4/7)(3/6)(2/5) = 4/35
bgb ---> (3/7)(4/6)(2/5) = 4/35

prob(as stated) = 4/35 + 4/35 = 8/35 or appr .229

To find the probability that the second defective bulb is found on the third selection, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Step 1: Calculate the total number of ways to select 3 bulbs out of 7.
We can use the combination formula for this calculation: nCr = n! / (r!(n-r)!)
In this case, selecting 3 bulbs out of 7 can be calculated as: 7C3 = 7! / (3!(7-3)!).
Simplifying this expression: 7C3 = 7! / (3!4!) = (7 x 6 x 5) / (3 x 2 x 1) = 35.

Step 2: Calculate the number of favorable outcomes.
To find the number of favorable outcomes, we need to consider the possible positions of the two defective bulbs (D) in the selection of 3 bulbs out of 7.
There are two possible positions for the second defective bulb:
- It could be in the second position (GDD) with one good bulb in the first position.
- It could be in the third position (GDG), with one good bulb in the first or second position.

For the first case (GDD), the total number of ways to select one good bulb from the four available is 4C1 = 4.
For the second case (GDG), the total number of ways to select one good bulb from the four available is 4C1 = 4, and the total number of ways to select one good bulb from the three remaining bulbs is 3C1 = 3.

Therefore, the number of favorable outcomes is: 4 + (4 x 3) = 16.

Step 3: Calculate the probability.
The probability is equal to the number of favorable outcomes divided by the total number of possible outcomes.
P(second defective bulb on third selection) = Number of favorable outcomes / Total number of possible outcomes
P(second defective bulb on third selection) = 16 / 35.

Therefore, the probability that the second defective bulb is found on the third selection is 16/35.

Sure, I can help you with that!

To find the probability that the second defective bulb is found on the third selection, we need to first analyze the possible outcomes.

There are a total of 7 bulbs in the box - 4 good ones and 3 defective ones. When we select a bulb without replacement, the total number of bulbs in the box decreases by 1 each time.

We want to find the probability that the second defective bulb is found on the third selection. Here's how we can approach this problem:

Step 1: Find the total number of possible outcomes for the first selection.
Since there are 7 bulbs in total, the first selection can be any of them. So, there are 7 possible outcomes for the first selection.

Step 2: Find the total number of possible outcomes for the second selection.
Once we have made the first selection, there are only 6 bulbs left in the box. Since we want to find the probability that the second defective bulb is found on the third selection, the second selection can be any of the remaining 6 bulbs. Therefore, there are 6 possible outcomes for the second selection.

Step 3: Find the total number of possible outcomes for the third selection.
After making the first and second selections, there are only 5 bulbs left in the box. Since we want to find the probability that the second defective bulb is found on the third selection, the third selection can be any of the remaining 5 bulbs. Therefore, there are 5 possible outcomes for the third selection.

Step 4: Multiply the number of outcomes together to find the total number of possible outcomes.
The total number of possible outcomes is calculated by multiplying the number of outcomes for each selection: 7 * 6 * 5.

Step 5: Find the total number of favorable outcomes.
In order to find the total number of favorable outcomes (i.e., the situations in which the second defective bulb is found on the third selection), we need to consider the specific ordering of the bulbs. There are 3 defective bulbs in total, and we want the second defective bulb to be found on the third selection. The first defective bulb could be selected in two different ways: before the second selection or after the second selection. However, the second defective bulb can only be selected ON the third selection. Therefore, there are 2 favorable outcomes.

Step 6: Calculate the probability.
The probability is calculated by dividing the total number of favorable outcomes by the total number of possible outcomes: favorable outcomes / possible outcomes.

In this case, the probability that the second defective bulb is found on the third selection is:
2 / (7 * 6 * 5) = 2 / 210 = 1/105 ≈ 0.0095

So, the probability is approximately 0.0095 or 1/105.

You start with 7 total and because you have already picked twice so you now have 5 left.

It wants the probability of the second defective light so that means of the two first picked one was good and one was defective.

Now you have 3 good lights and 2 defective lights.

the probability of picking a defective light would be 2/5 =0.4