# NCERT Class 12-Mathematics: Chapter – 13 Probability Part 8 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 14**:

Three dice are thrown at the same-time. Find the probability of getting three two՚s, if it is known that the sum of the numbers on the dice was six.

**Answer**:

On a throw of three dice, we have sample space

Let is the event when the sum of numbers on the dice was six and is the event when three two՚s occurs.

Also,

**Question 15**:

Suppose 10,000 tickets are sold in a lottery each for Re 1. First prize is of ₹ 3000 and the second prize is of ₹ 2000. There are three third prizes of ₹ 500 each. If you buy one ticket, what is your expectation.

**Answer**:

Let x is the random variable for the prize.

Since,

**Question 16**:

A bag contains 4 white and 5 black balls. Another bag contains 9 white and 7 black balls. A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag. Find the probability that the ball drawn is white.

**Answer**:

**Question 17**:

Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag and a ball is selected at random. Determine the probability of selecting a black ball.

**Answer**:

**Question 18**:

A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also not noted. Then another ball is drawn at random. What is the probability of second ball being blue?

**Answer**:

**Question 19**:

Four cards are successively drawn without replacement from a deck of playing cards. What is the probability that all the four cards are kings?

**Answer**:

**Question 20**:

A die is thrown times. Find the probability that an odd number will come up exactly three times.

**Answer**:

**Question 21**:

Ten coins are tossed. What is the probability of getting at least 8 heads?

**Answer**:

**Question 22**:

The probability of a man hitting a target is . He shoots 7 times. What is the probability of his hitting at least twice?

**Answer**:

**Question 23**:

A lot of 100 watches is known to have 10 defective watches. If 8 watches are selected (one by one with replacement) at random, what is the probability that there will be at least one defective watch?

**Answer**:

Probability of defective watch from a lot of watches