Advertisements
Advertisements
Question
Three coins are tossed once. Find the probability of getting
- 3 heads
- 2 heads
- at least 2 heads
- at most 2 heads
- no head
- 3 tails
- exactly two tails
- no tail
- atmost two tails.
Solution
If 3 coins are tossed, then the sample space of the experiment is
S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Total possible outcomes = 8
(i) Three heads {HHH} can appear in one way.
So the probability of getting 3 heads = `1/8`
(ii) There are three ways of getting 2 heads or 2 heads 1 tail, HHT, HTH, THH.
Total possible outcomes = 8
Probability of 2 heads appearing = `3/8`
(iii) To get a minimum of 2 heads, 2 heads 1 tail or 3 heads will occur
∴ A minimum of 2 heads can appear in four ways, HHT, HTH, THH, HHH.
Hence, the probability of minimum 2 heads appearing = `4/8`
= `1/2`
(iv) Maximum 2 heads will appear as follows.
(a) No head or three tails
(b) One head 2 tails
(c) 2 heads 1 tail
This {TIT, HTT, THT, TTH, HHT, HTH, THH} can appear in seven ways.
Total possible outcomes = 8
∴ Probability of maximum 2 heads appearing = `7/8`
(v) No head appearing means three tails appearing, which can happen in one way (TTT).
Total possible outcomes = 8
Hence, the probability of no head appearing = `1/8`
(vi) Three tails can appear in one way (TTT).
Probability of three tails appearing = `1/8`
(vii) Actually 2 tails (TTH, THT, HTT) can be obtained in three ways.
Total possible outcomes = 8
∴ Probability of two tails appearing = `3/8`
(viii) No tails means all three heads appear, so (HHH) can happen in only 1 way.
Total possible outcomes = 8
Probability of no tails appearing = `1/8`
(ix) Maximum two tails appearing
⇒ All three tails do not appear.
Probability of all three tails appearing = `1/8`
∴ Probability of maximum two tails appearing = 1 – (Probability of all three tails appearing)
= `1 - 1/8`
= `7/8`
APPEARS IN
RELATED QUESTIONS
A coin is tossed twice, what is the probability that at least one tail occurs?
A die is thrown, find the probability of following events:
- A prime number will appear,
- A number greater than or equal to 3 will appear,
- A number less than or equal to one will appear,
- A number more than 6 will appear,
- A number less than 6 will appear.
A card is selected from a pack of 52 cards.
- How many points are there in the sample space?
- Calculate the probability that the card is an ace of spades.
- Calculate the probability that the card is
- an ace
- black card.
A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12
There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?
Check whether the following probabilities P(A) and P(B) are consistently defined
P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6
Fill in the blank in following table:
| P(A) | P(B) | P(A ∩ B) | P(A ∪ B) |
| 0.5 | 0.35 | .... | 0.7 |
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 all will be blue?
4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, the digits are repeated?
The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?
Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.
A bag contains 5 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both balls are red or both are black?
If a letter is chosen at random from the English alphabet, find the probability that the letter is a vowel .
Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S = {w1, w2, w3, w4, w5, w6, w7}:
| Elementary events: | w1 | w2 | w3 | w4 | w5 | w6 | w7 |
| (iii) | 0.7 | 0.06 | 0.05 | 0.04 | 0.03 | 0.2 | 0.1 |
In a single throw of three dice, find the probability of getting the same number on all the three dice.
A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability thatat least one is defective
An urn contains twenty white slips of paper numbered from 1 through 20, ten red slips of paper numbered from 1 through 10, forty yellow slips of paper numbered from 1 through 40, and ten blue slips of paper numbered from 1 through 10. If these 80 slips of paper are thoroughly shuffled so that each slip has the same probability of being drawn. Find the probabilities of drawing a slip of paper that is blue or white
One mapping (function) is selected at random from all the mappings of the set A = {1, 2, 3, ..., n} into itself. The probability that the mapping selected is one to one is ______.
Six new employees, two of whom are married to each other, are to be assigned six desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have nonadjacent desks?
The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P(A ∩ B) = .07). Determine P(A)
The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P(A ∩ B) = .07). Determine `P(B ∩ barC)`
The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P(A ∩ B) = .07). Determine P(B ∩ C)
The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P(A ∩ B) = .07). Determine Probability of exactly one of the three occurs
If the letters of the word ASSASSINATION are arranged at random. Find the probability that four S’s come consecutively in the word
If the letters of the word ASSASSINATION are arranged at random. Find the probability that no two A’s are coming together
In a non-leap year, the probability of having 53 tuesdays or 53 wednesdays is ______.
Three numbers are chosen from 1 to 20. Find the probability that they are not consecutive ______.
While shuffling a pack of 52 playing cards, 2 are accidentally dropped. Find the probability that the missing cards to be of different colours ______.
Without repetition of the numbers, four-digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is ______.
6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is ______.
A single letter is selected at random from the word ‘PROBABILITY’. The probability that it is a vowel is ______.
The probability that a student will pass his examination is 0.73, the probability of the student getting a compartment is 0.13, and the probability that the student will either pass or get compartment is 0.96.
| C1 Probability |
C2 Written Description |
| (a) 0.95 | (i) An incorrect assignment |
| (b) 0.02 | (ii) No chance of happening |
| (c) – 0.3 | (iii) As much chance of happening as not |
| (d) 0.5 | (iv) Very likely to happen |
| (e) 0 | (v) Very little chance of happening |
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 atleast one will be green?
