Please help...
In a 200 m swimming race between 8 boys, the probability of Omar winning the race if he is in one of the two outside lanes is 1/4. If he is in any of the other lanes, the probability of Omar winning is 1/3.
If the lanes are drawn at random, what is the overall probability of Omar winning the race?
Thank you
Consider that there are 2/8 probability of getting an outside lane. To get the probability that both (all) events would happen, you need to multiply the probabilities of the individual events (2/8*1/4).
Do the same for the 6 inside lanes.
However, he can be placed in either the inside or outside lanes. In the case of "either-or" probabilities, you add the probabilities of the individual events.
I hope this helps. Thanks for asking.
To find the overall probability of Omar winning the race, we need to consider two scenarios: when Omar is in one of the outside lanes and when he is in one of the inside lanes.
First, let's consider the probability of Omar winning if he is in one of the two outside lanes, which is given as 1/4. Since there are 8 lanes in total and 2 of them are outside lanes, the probability of Omar being in one of the outside lanes is 2/8.
Next, let's consider the probability of Omar winning if he is in any of the other 6 inside lanes, which is given as 1/3. There are 8 lanes in total, and 6 of them are inside lanes, so the probability of Omar being in one of the inside lanes is 6/8.
To calculate the overall probability of Omar winning, we need to consider the probability of each scenario occurring and add them together.
For the outside lanes case: Probability of Omar being in an outside lane (2/8) multiplied by the probability of winning if in an outside lane (1/4) = (2/8) * (1/4) = 1/16.
For the inside lanes case: Probability of Omar being in an inside lane (6/8) multiplied by the probability of winning if in an inside lane (1/3) = (6/8) * (1/3) = 3/16.
Now, to find the overall probability of Omar winning, we add the probabilities of each scenario together:
Overall probability = Probability of winning in outside lanes + Probability of winning in inside lanes = 1/16 + 3/16 = 4/16 = 1/4.
Therefore, the overall probability of Omar winning the race, when the lanes are drawn at random, is 1/4.
I hope this clarifies the solution for you. Let me know if there's anything else I can assist you with!
To calculate the overall probability of Omar winning the race, we need to consider two scenarios: when Omar is in one of the two outside lanes and when he is in any of the other lanes.
Scenario 1: Omar is in one of the two outside lanes.
- Probability of Omar winning in this scenario is 1/4.
Scenario 2: Omar is in any of the other lanes.
- Probability of Omar winning in this scenario is 1/3.
Now, we need to calculate the probability of each scenario occurring.
The probability of Omar being in one of the two outside lanes is 2 out of 8, which can be expressed as 2/8 or 1/4.
The probability of Omar being in any of the other lanes is 6 out of 8, which can be expressed as 6/8 or 3/4.
To calculate the overall probability of Omar winning the race, we use the law of total probability:
Overall probability = (Probability of Scenario 1) * (Probability of Omar winning in Scenario 1) + (Probability of Scenario 2) * (Probability of Omar winning in Scenario 2)
Overall probability = (1/4) * (2/8) + (3/4) * (1/3)
Simplifying this expression:
Overall probability = (1/8) + (3/12)
Overall probability = 1/8 + 1/4
Overall probability = 2/8 + 2/8
Overall probability = 4/8
Overall probability = 1/2
Therefore, the overall probability of Omar winning the race is 1/2 or 50%.
I hope this explanation helps! If you have any more questions, feel free to ask.