# Probability Problems: Find the Answer ASAP

• rakesh1988
In summary, probability is a mathematical concept used to measure the likelihood of an event occurring, allowing for informed decisions and predictions. There are three types of probability: theoretical, experimental, and subjective. To calculate probability, you divide the number of desired outcomes by the total number of possible outcomes. Independent events do not affect each other's outcomes, while dependent events do. In real-life situations, probability is used for predicting weather, analyzing stock markets, and making decisions in games of chance. It is also utilized in fields such as insurance, medicine, and sports to assess risk and make informed decisions.
rakesh1988
1. box 'a' contains 2 white and 4 black balls, box 'b' contains 5 white and 7 black balls. a ball is transferred from a to b. then a ball is drawn from b. I) what is the probability that it is white? II) and it is black?

2.find the prob that in a random arrangement of the word UNIVERSITY, 2I's do not come together

pls help me in solving these problem ASAP... its urgent

Welcome to PF rakesh. Unfortunately you have overwritten that terribly handy template that comes up when you try to post here, so I do not know what you have tried already. But let me give you a hint:
P(drawing a white ball) = P(drawing a white ball | a white ball was transferred from a to b) + P(drawing a white ball | a black ball was transferred from a to b).

For the second one, I suggest checking how many rearrangements of the letters there are and how many there are in which the two I's are together.

Solution:

box A contains
2W 4B

box B contains
5W 7B

Step 1)

When a ball is transferred from A to B

= For box A: P(w) = Number of chances you might get white (Events)/ Total number chances = 2 / 6 = 1/3

= For box A: P(b) = 4 / 6 = 2 / 3

-----------------------------------------------------------------------

Step 2)

Now, assuming White is Transferred from A to B
B contains:
6W 7B

So For box B: p(w)= 6 / 13

Now, assuming Black is Transferred from A to B
B contains:
5W 8B

So For box B: p(b)= 8 / 13
-----------------------------------------------------------------------

Step 3:

Probability of box B is dependent on probability of box A.

So formula for dependent or probability is

Total Probability = P(A).P(B|A)

P(B|A) means Probability of box B Assuming Probability of box A

So

Ans
1) Probablity that is white = Box A P(w) * Box A P(w) = 1/3 * 6/13 = 6/39 = 2/13

2) Probablity that is black = Box A P(b) * Box A P(b) = 2/3 * 8/13 = 16/39

is this ok?? pls help

Step 1 and 2 look correct, although your answer is not going entirely as it should

Let's look at the probability P(W) that a ball you draw is white. Then
P(W) = P(W | W) + P(W | B)
where P(W | A) means: the probability of drawing a white, given that color A (either W(hite) or B(lack)) was transferred. In step 1 and 2 you have reasoned that, for example
P(W | W) = P(transferring a white ball from A to B) * P(drawing a white ball from B, after a white ball was added) = 2/6 * 6/13
and
P(W | B) = P(transferring a black ball from A to B) * P(drawing a white ball from B, after a black ball was added) = 4/6 * 5/13.

So you get
P(W) = 2/6 * 6/13 + 4/6 * 5/13 = (6 + 10) / 39 = 16/39
which seems to be what you have with P(B).

Also note how your answer cannot be correct: whatever ball you transfer, when you draw from B it must be either black or white. So P(W) + P(B) = 1, which your answer does not satisfy (2/13 + 16/39 = 22/39 =/= 1).

I think your mistake is in the formula
P(B) = P(B | A) . P(A)
which should actually be
P(B) = Sum[over all possibilities in A]( P(B | A) P(A) )
so in this case
P(B) = P(2W,5B in A) P(draw white from B | 2W, 5B in A) + P(3W, 4B in A) P(draw white from B | 3W, 4B in A).

## What is probability and why is it important?

Probability is a mathematical concept used to measure the likelihood of an event occurring. It is important because it allows us to make informed decisions and predictions based on the likelihood of different outcomes.

## What are the different types of probability?

There are three types of probability: theoretical, experimental, and subjective. Theoretical probability is based on mathematical principles and is used for predicting outcomes in ideal situations. Experimental probability is based on data from experiments and observations. Subjective probability is based on personal beliefs and opinions.

## How do you calculate probability?

To calculate probability, you divide the number of desired outcomes by the total number of possible outcomes. This will give you a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

## What is the difference between independent and dependent events?

Independent events are events where the outcome of one event does not affect the outcome of another event. Dependent events are events where the outcome of one event does affect the outcome of another event.

## How can probability be used in real-life situations?

Probability can be used in many real-life situations, such as predicting the weather, analyzing stock market trends, and making decisions in games of chance. It is also used in fields such as insurance, medicine, and sports to make informed decisions and assess risk.

Replies
2
Views
3K
Replies
2
Views
1K
Replies
9
Views
5K
Replies
13
Views
1K
Replies
9
Views
1K
Replies
1
Views
1K
Replies
6
Views
2K
Replies
2
Views
2K
Replies
10
Views
1K
Replies
3
Views
325