English

Three Coins Are Tossed Together. Find the Probability of Getting:(I) Exactly Two Heads - Mathematics

Advertisements
Advertisements

Question

Three coins are tossed together. Find the probability of getting exactly two heads

Solution

When three coins are tossed once, the sample space is given by
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
i.e. (S) = 8

 Let E1 = event of getting exactly two heads
Then E1 = {HHT, HTH, THH}
i.e. n(E1) = 3

\[\therefore P\left( E_1 \right) = \frac{n\left( E_1 \right)}{n\left( S \right)} = \frac{3}{8}\]

 

shaalaa.com
Probability - Probability of 'Not', 'And' and 'Or' Events
  Is there an error in this question or solution?
Chapter 33: Probability - Exercise 33.3 [Page 46]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 33 Probability
Exercise 33.3 | Q 4.1 | Page 46

RELATED QUESTIONS

If `2/11` is the probability of an event, what is the probability of the event ‘not A’.


A letter is chosen at random from the word ‘ASSASSINATION’. Find the probability that letter is

  1. a vowel
  2. an consonant

If E and F are events such that P(E) = `1/4`, P(F) = `1/2` and P(E and F) = `1/8`, find

  1. P(E or F)
  2. P(not E and not F).

A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine P(not A).


In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both?


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

  1. The student opted for NCC or NSS.
  2. The student has opted neither NCC nor NSS.
  3. The student has opted NSS but not NCC.

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

  1. P(2)
  2. P(1 or 3)
  3. P(not 3)

Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.


In a simultaneous throw of a pair of dice, find the probability of getting a doublet of prime numbers


In a simultaneous throw of a pair of dice, find the probability of getting a sum greater than 9


In a simultaneous throw of a pair of dice, find the probability of getting an even number on one and a multiple of 3 on the other


In a simultaneous throw of a pair of dice, find the probability of getting a sum more than 6


In a simultaneous throw of a pair of dice, find the probability of getting neither a doublet nor a total of 10


In a simultaneous throw of a pair of dice, find the probability of getting odd number on the first and 6 on the second


In a simultaneous throw of a pair of dice, find the probability of getting a total greater than 8.

 

Three coins are tossed together. Find the probability of getting at least two heads


A box contains 6 red marbles numbered 1 through 6 and 4 white marbles numbered from 12 through 15. Find the probability that a marble drawn is even numbered


Fill in the blank in the table:

P (A) P (B) P (A ∩ B) P(A∪ B)
\[\frac{1}{3}\] \[\frac{1}{5}\] \[\frac{1}{15}\] ......

Fill in the blank in the table:

P (A) P (B) P (A ∩ B) P(A∪ B)
0.35 .... 0.25 0.6

Fill in the blank in the table:

P (A) P (B) P (A ∩ B) P(A∪ B)
0.5 0.35 ..... 0.7

If A and B are two events associated with a random experiment such that
P(A) = 0.5, P(B) = 0.3 and P (A ∩ B) = 0.2, find P (A ∪ B).


A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.


The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English Examination is 0.75. What is the probability of passing the Hindi Examination?


100 students appeared for two examination, 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has passed at least one examination.


One of the two events must occur. If the chance of one is 2/3 of the other, then odds in favour of the other are


The probability that a leap year will have 53 Fridays or 53 Saturdays is


A person write 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is


A and B are two events such that P (A) = 0.25 and P (B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is


If the probability of A to fail in an examination is \[\frac{1}{5}\]  and that of B is \[\frac{3}{10}\] . Then, the probability that either A or B fails is

 
 

A box contains  10 good articles and 6 defective articles. One item is drawn at random. The probability that it is either good or has a defect, is


Two dice are thrown simultaneously. The probability of getting a pair of aces is


Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floor is


A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is


One mapping is selected at random from all mappings of the set A = {1, 2, 3, ..., n} into itself. The probability that the mapping selected is one to one is


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 10 tickets.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×