Exploring the Probability of Drawing a Black Ball

The figures in the tree diagram show the probabilities of each path, which are necessary to calculate the conditional probability of drawing a black ball given that urn I is chosen.
  • #1
oufa
26
0
hi
i have an exam after 1 week and while i was studying i found this simple problem
but i couldn't answer it as the author
it is


We have two urns, I and II. Urn I contains 2 black balls and 3 white
balls. Urn II contains 1 black ball and 1 white ball. An urn is drawn at random
and a ball is chosen at random from it. We can represent the sample space of this
experiment as the paths through a tree as shown in Figure 4.1. The probabilities
assigned to the paths are also shown.
Let B be the event “a black ball is drawn,” and I the event “urn I is chosen.”
Then the branch weight 2/5, which is shown on one branch in the figure, can now
be interpreted as the conditional probability P(B|I).



any one please tell me why it is 2/5 because i think it is 1/5
figures mentioned arenot important in solving it

thnx for help
 
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  • #2
Why do you think it should be 1/5 and why do you think the figures are not important?

The "branch weight" is 2/5 precisely because urn I contains 5 balls, 2 of which are black.
 

Related to Exploring the Probability of Drawing a Black Ball

1. What is the definition of probability?

Probability is the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

2. How is probability calculated?

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In the case of drawing a black ball from a bag, the probability would be the number of black balls in the bag divided by the total number of balls in the bag.

3. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability, on the other hand, is based on actual observations and can vary depending on the sample size and the number of trials conducted.

4. How can we increase the probability of drawing a black ball?

The probability of drawing a black ball can be increased by having more black balls in the bag, or by decreasing the total number of balls in the bag. Another way to increase probability is by conducting multiple trials and keeping track of the outcomes.

5. How does the probability of drawing a black ball change if we replace the balls after each draw?

If the balls are replaced after each draw, the probability of drawing a black ball remains the same for each draw. This is because the total number of balls and the number of black balls in the bag remain constant. Each draw is considered an independent event, so the probability remains unchanged.

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