Advertisements
Advertisements
Question
Select the correct option from the given alternatives :
There are 5 girls and 2 boys, then the probability that no two boys are sitting together for a photograph is
Options
`1/21`
`4/7`
`2/7`
`5/7`
Solution
`5/7`
Explanation;
There are 5 girls and 2 boys. They can be arranged among themselves in 7P7 = 7! ways.
∴ Girls can be arranged among themselves in 5P5 = 5! ways.
No two boys should sit together
Let girls be denoted by letter G.
– G – G – G – G – G–
There are 6 places, marked by ‘__’ where boys can sit.
∴ Boys can be arranged in 6P2 = `(6!)/((6 - 2)!`
= `(6 xx 5 xx 4!)/(4!)`
= 30 ways.
∴ Required probability = `(5! xx 30)/(7!)`
= `(5! xx 30)/(7 xx 6 xx 5!)`
= `5/7`.
APPEARS IN
RELATED QUESTIONS
A fair die is thrown two times. Find the probability that the first throw gives a multiple of 2 and the second throw gives a multiple of 3.
Two cards are drawn from a pack of 52 cards. Find the probability that one is club and the other is a diamond.
Two cards are drawn from a pack of 52 cards. Find the probability that both are red cards
Two cards are drawn from a pack of 52 cards. Find the probability that one is a heart card and the other is a non-heart card
Three cards are drawn from a pack of 52 cards. Find the chance that two are queen cards and one is an ace card
Three cards are drawn from a pack of 52 cards. Find the chance that at least one is a diamond card
Three cards are drawn from a pack of 52 cards. Find the chance that all are from the same suit
Find the probability of getting both red balls, when from a bag containing 5 red and 4 black balls, two balls are drawn, with replacement
Find the probability of getting both red balls, when from a bag containing 5 red and 4 black balls, two balls are drawn, without replacement
Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement vowels are always together.
Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement starting with a vowel and end with a consonant
A bag contains 7 black and 4 red balls. If 3 balls are drawn at random find the probability that all are black
A bag contains 7 black and 4 red balls. If 3 balls are drawn at random find the probability that one is black and two are red.
Two fair dice are thrown. Find the probability that number on the upper face of the first die is 3 or sum of the numbers on their upper faces is 6
A bag contains 5 red, 4 blue and an unknown number m of green balls. If the probability of getting both the balls green, when two balls are selected at random is `1/7`, find m
A number is drawn at random from the numbers 1 to 50. Find the probability that it is divisible by 2 or 3 or 10
Select the correct option from the given alternatives :
Two dice are thrown simultaneously. Then the probability of getting two numbers whose product is even is
Solve the following:
A die is loaded in such a way that the probability of the face with j dots turning up is proportional to j for j = 1, 2, .......6. What is the probability, in one roll of the die, that an odd number of dots will turn up?
Solve the following:
Suppose that five good fuses and two defective ones have been mixed up. To find the defective fuses, we test them one-byone, at random and without replacement. What is the probability that we are lucky and fine both of the defective fuses in the first two tests?
Solve the following:
A family has two children. One of them is chosen at random and found that the child is a girl. Find the probability that both the children are girls given that at least one of them is a girl
Four persons work independently on a task. If the respective probabilities that they will solve it are 1/5, 1/3, 1/7, and 1/6, then the probability that none can solve it is ______
A coin is tossed 9 times. The probability of obtaining at most one head is ______
A coin is tossed 9 times. The probability of obtaining at most one head is ______
If three dices are thrown then the probability that the sum of the numbers on their uppermost faces to be atleast 5 is ______.
There are two bags. One bag contains 4 blue pens and 3 black pens. The other bag contains 7 red pens and 3 black pens. If a bag is selected at random and from it, a pen is drawn, the probability that the pen is black is ______
An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is ______.
A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is ______.
A cupboard contains 3 pink, 3 black and 5 blue shirts well mixed. A person pulls out 2 shirts at random from cupboard. The probability that they match is ______.
In a simultaneous toss of five coins, the probability of getting exactly four tails is ______.
A die is rolled. If X denotes the number of positive divisors of the outcome then the range of the random variable X is ______.
A die is thrown four times. The probability of getting perfect square in at least one throw is ______.
Probability that a person will develop immunity after vaccinations is 0.8. if 8 people are given the vaccine, then probability that all develop immunity is = ______.
Probability of guessing correctly atleast 7 out of 10 answers in a ‘True’ or ‘False’ test is equal to ______.
