# NCERT Class 11 Mathematics Solutions: Chapter 16 – Probability Miscellaneous Exercise Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. A box contains red marbles, blue marbles and green marbles. Marbles are drawn from the box, what is the probability that

(i) all will be blue?

(ii) at least one will be green?

Answer:

Total number of marbles

Number of ways of drawing marbles from marbles

Answer: (i)

All the drawn marbles will be blue if we draw marbles out of blue marbles.

5 blue marbles can be drawn from blue marbles in ways.

Probability that all marbles will be blue

Answer: (ii)

Number of ways in which the drawn marble is not green

Probability that no marble is green

Probability that at least one marble is green

2. cards are drawn from a well-shuffled deck of cards. What is the probability of obtaining diamonds and one spade?

Answer:

Number of ways of drawing cards from cards

In a deck of cards, there are diamonds and spades.

Number of ways of drawing diamonds and one spade

The probability of obtaining diamonds and one spade

3. A die has two faces each with number , three faces each with number and one face with number . If die is rolled once, determine

(i)

(ii)

(iii)

Answer:

Total number of faces

Answer: (i)

Number faces with number

Answer: (ii)

Answer: (iii)

Number of faces with number

So,