Q2 of 54 Page 408

4 cards are drawn from a well – shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?

Number of ways of drawing 4 cards from 52 cards = 52C4

In a deck of 52 cards, there are 13 diamonds and 13 spades.


Number of ways of drawing 3 diamonds and one spade = 13C3 × 13C1


Thus, the probability of obtaining 3 diamonds and one spade


= (13C3 × 13C1)/ 52C4


More from this chapter

All 54 →
21

In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that

(i) The student opted for NCC or NSS.


(ii) The student has opted neither NCC nor NSS.


(iii) The student has opted NSS but not NCC.

 1

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that

(i) all will be blue? (ii) at least one will be green?

 3

A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine

(i) P(2) (ii) P(1 or 3) (iii) P(not 3)

 4

In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy (a) one ticket (b) two tickets (c) 10 tickets.