Suppose a bag contains 3 blue and 2 green marbles. You randomly draw 2 marbles without replacement. If B=drawing a blue marble and G=drawing a green marble, which event does NOT have the same probability as the others?
Bag
A. GG
B. BB
C. GB
D. BG
Q 1. GG
Q 2. P(B, then G)
Q 3. 4/6 (dot) 4/6
Q 4. 2/6 (dot) 1/5
Q 5. 1 green and 3 blue
THANK YOU JJ
Where is your attempt to do this?
Can someone tell meh le answers for connexus gizmos??? The first question is the one this person asked here.
Suppose a bag contains 3 blue and 2 green marbles. You randomly draw 2 marbles without replacement. If B=drawing a blue marble and G=drawing a green marble, which event does NOT have the same probability as the others?
Hmm, let me think about this colorful conundrum for a moment. In order to find the probability of each event, we need to consider the total number of outcomes and the number of favorable outcomes.
Let's break it down step by step, shall we?
A. GG: There are 2 green marbles, so the probability of drawing the first green marble is 2/5. After that, only 1 green marble remains, so the probability of drawing another green marble is 1/4. So the probability of drawing 2 green marbles would be (2/5) * (1/4) = 1/10.
B. BB: There are 3 blue marbles, so the probability of drawing the first blue marble is 3/5. After that, only 2 blue marbles remain, so the probability of drawing another blue marble is 2/4. Therefore, the probability of drawing 2 blue marbles would be (3/5) * (2/4) = 3/10.
C. GB: There are 3 blue marbles and 2 green marbles, so the probability of drawing a green marble is 2/5 and the probability of drawing a blue marble is 3/5. Therefore, the probability of drawing a green marble followed by a blue marble would be (2/5) * (3/4) = 6/20 = 3/10.
D. BG: This event is equivalent to event C, where we draw a blue marble followed by a green marble. We already calculated the probability for event C as 3/10.
So, after all that number crunching, it seems that the event that does NOT have the same probability as the others is B. BB, with a probability of 3/10.
Remember, probability is fun, but always keep an eye out for those sneaky marbles!
To determine which event does not have the same probability as the others, we need to calculate the probability of each event.
Since we are randomly drawing 2 marbles without replacement, the total number of possible outcomes is given by the combination formula. We can calculate this as:
Total number of outcomes = (total number of marbles) choose (number of marbles drawn)
= (5 choose 2)
= 5! / (2! * (5 - 2)!)
= 10
Now, let's calculate the probability of each event:
A. GG: Probability of drawing a green marble followed by another green marble
There are 2 green marbles out of a total of 5 marbles in the bag. After drawing the first green marble, the bag contains 4 marbles, including 1 green marble. Therefore, the probability of drawing a green marble followed by another green marble is:
Probability = (2/5) * (1/4) = 2/20 = 1/10
B. BB: Probability of drawing a blue marble followed by another blue marble
There are 3 blue marbles out of a total of 5 marbles in the bag. After drawing the first blue marble, the bag contains 4 marbles, including 2 blue marbles. Therefore, the probability of drawing a blue marble followed by another blue marble is:
Probability = (3/5) * (2/4) = 6/20 = 3/10
C. GB: Probability of drawing a green marble followed by a blue marble
There are 2 green marbles and 3 blue marbles in the bag. After drawing the first green marble, the bag contains 4 marbles, including 3 blue marbles. Therefore, the probability of drawing a green marble followed by a blue marble is:
Probability = (2/5) * (3/4) = 6/20 = 3/10
D. BG: Probability of drawing a blue marble followed by a green marble
This event is the same as event C, where we draw a green marble followed by a blue marble. Since we are calculating probabilities and the order of marbles doesn't matter, the probability is the same: 3/10.
Comparing the probabilities of all the events, we see that event A (GG) has a probability of 1/10, while all the other events (BB, GB, BG) have a probability of 3/10. Therefore, event A does not have the same probability as the others.