NCERT Class 12-Mathematics: Chapter –13 Probability Part 13

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Question 44:

A letter is known to have come either from TATA NAGAR or from CALCUTTA. On the envelope, just two consecutive letter TA are visible. What is the probability that the letter came from TATA NAGAR.

Answer:

Let be the event that letter is from TATA NAGAR and be the event that letter is from CALCUTTA.

Also, let be the event on the letter, two consecutive letters TA are visible.

And

Since, if letter is from TATA NAGAR, we see that the events of two consecutive letters visible are and if letter is from CALCUTTA, we see that the events of two consecutive letters to visible are , So,

Question 45:

There are two bags, one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls. A die is thrown. If it shows up 1 or 3, a ball is taken from the 1st bag; but it shows up any other number, a ball is chosen from the second bag. Find the probability of choosing a black ball.

Answer:

Since,

Let be the event that bag I is selected and be the event that bag II is selected.

Let be the event that black ball is chosen.

And

Question 46:

There are three urns containing 2 white and 3 black balls, 3 white and 2 black balls, and 4 white and 1 black balls, respectively. There is an equal probability of each urn being chosen. A ball is drawn at random from the chosen urn and it is found to be white. Find the probability that the ball drawn was from the second urn.

Answer:

Let

And

Let be the event that a ball is chosen from urn be the event that a ball is chosen from urn be the event that a ball is chosen from urn .

Also,

Now, let be the event that white ball is drawn.

Now,

Question 47:

By examining the chest X ray, the probability that TB is detected when a person is actually suffering is . The probability of an healthy person diagnosed to have TB is . In a certain city, 1 in people suffers from TB. A person is selected at random and is diagnosed to have TB. What is the probability that he actually has TB?

Answer:

Let

And