Advertisements
Advertisements
Question
Solve the following:
A letter is taken at random from the letters of the word 'ASSISTANT' and another letter is taken at random from the letters of the word 'STATISTICS'. Find the probability that the selected letters are the same
Advertisements
Solution
Word ASSISTANT has 2A, I, N, 3S, 2T and
word STATISTICS has A, C, 2I, 3S, 3T.
C and N are uncommon letters.
In words ASSISTANT, there are 9 letters out of which 2 letters are ‘A’ and in word STATISTICS, there are 10 letters, out of which 1 letter is A.
∴ Probability of choosing A from both the letters
= `(""^2"C"_1)/(""^9"C"_1) xx (""^1"C"_1)/(""^10"C"_1)`
= `2/9 xx 1/10`
= `1/45`
Similarly,
Probability of choosing I from both the letters
= `(""^1"C"_1)/(""^9"C"_1) xx (""^2"C"_1)/(""^10"C"_1)`
= `1/9xx2/10`
= `1/45`
Probability of choosing S from both the letters
= `(""^3"C"_1)/(""^9"C"_1) xx (""^3"C"_1)/(""^10"C"_1)`
= `3/9xx3/10`
= `1/10`
Probability of choosing T from both the letters
= `(""^2"C"_1)/(""^9"C"_1) xx (""^3"C"_1)/(""^10"C"_1)`
= `2/9 xx 3/10`
= `1/15`
∴ Required probability = `1/45 + 1/45 + 1/10 + 1/15`
= `19/90`
APPEARS IN
RELATED QUESTIONS
There are four pens: Red, Green, Blue, and Purple in a desk drawer of which two pens are selected at random one after the other with replacement. State the sample space and the following event.
A: Selecting at least one red pen.
There are four pens: Red, Green, Blue, and Purple in a desk drawer of which two pens are selected at random one after the other with replacement. State the sample space and the following event.
B: Two pens of the same color are not selected.
A coin and a die are tossed simultaneously. Enumerate the sample space and the following event.
A: Getting a Tail and an Odd number
A coin and a die are tossed simultaneously. Enumerate the sample space and the following event.
B: Getting a prime number
Find n(S) of the following random experiment.
5 letters are to be placed into 5 envelopes such that no envelope is empty.
Find n(S) of the following random experiment.
3 tickets are drawn from a box containing 20 lottery tickets.
Two fair dice are thrown. State the sample space and write favorable outcomes for the following event:
A: Sum of numbers on two dice is divisible by 3 or 4
Two fair dice are thrown. State the sample space and write favorable outcomes for the following event:
B: Sum of numbers on two dice is 7
A bag contains four cards marked as 5, 6, 7, and 8. Find the sample space if two cards are drawn at random with replacement.
From a bag containing 10 red, 4 blue and 6 black balls, a ball is drawn at random. Find the probability of drawing a red ball.
From a bag containing 10 red, 4 blue and 6 black balls, a ball is drawn at random. Find the probability of drawing a blue or black ball
A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. Find the probability that, Number on the ticket is divisible by 6
A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. Find the probability that, Number on the ticket is a perfect square
A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. Find the probability that, Number on the ticket is prime
A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. Find the probability that, Number on the ticket is divisible by 3 and 5
What is the chance that a leap year, selected at random, will contain 53 Sundays?
A room has three sockets for lamps. From a collection 10 bulbs of which 6 are defective. At night a person selects 3 bulbs, at random and puts them in sockets. What is the probability that the room is lit
Select the correct option from the given alternatives :
In a jar there are 5 black marbles and 3 green marbles. Two marbles are picked randomly one after the other without replacement. What is the possibility that both the marbles are black?
Solve the following:
The letters of the word 'EQUATION' are arranged in a row. Find the probability that All the vowels are together
Solve the following:
The letters of the word 'EQUATION' are arranged in a row. Find the probability that Arrangement starts with a vowel and ends with a consonant
Solve the following:
Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is and even number?
Solve the following:
If the letters of the word 'REGULATIONS' be arranged at random, what is the probability that there will be exactly 4 letters between R and E?
Solve the following:
In how many ways can the letters of the word ARRANGEMENTS be arranged? Find the chance that an arrangement chosen at random begins with the letters EE.
A player tosses 2 fair coins. He wins Rs. 5 If 2 heads appear, Rs. 2 If 1 head appear and Rs.1 if no head appears, then variance of his winning amount is ______.
If three fair coins are tossed, where X = number of tails obtained, then Var(X) is ______
In a bike race, the odds against three bikes are 3 : 1, 2 : 1, and 4 : 1. The probability that one of the bikes will win the race is ______
Three randomly chosen non-negative integer x, y and z are found to satisfy the equation x + y + z = 10. Then, the probability that z is even, is ______.
Two events A and B have probabilities 0.25 and 0.50, respectively. The probability that both A and B occur simultaneously is 0.14. Then, the probability that neither A nor B occurs, is ______.
