Advertisements
Advertisements
प्रश्न
A fair coin is tossed 8 times, find the probability of at least six heads
उत्तर
Let X denote the number of heads obtained when a fair is tossed 8 times.
Now, X is a binomial distribution with n = 8, \[p = \frac{1}{2}\] and \[q = 1 - \frac{1}{2} = \frac{1}{2}\] .
\[ = P\left( X = 6 \right) + P\left( X = 7 \right) + P\left( X = 8 \right)\]
\[ =^8 C_6 \left( \frac{1}{2} \right)^8 +^8 C_7 \left( \frac{1}{2} \right)^8 +^8 C_8 \left( \frac{1}{2} \right)^8 \]
\[ = \left( 28 + 8 + 1 \right) \times \frac{1}{256}\]
\[ = \frac{37}{256}\]
APPEARS IN
संबंधित प्रश्न
There are 6% defective items in a large bulk of items. Find the probability that a sample of 8 items will include not more than one defective item.
An urn contains 25 balls of which 10 balls are red and the remaining green. A ball is drawn at random from the urn, the colour is noted and the ball is replaced. If 6 balls are drawn in this way, find the probability that:
(i) All the balls are red.
(ii) Not more than 2 balls are green.
(iii) The number of red balls and green balls is equal.
In a bolt factory, three machines A, B, and C manufacture 25%, 35% and 40% of the total production respectively. Of their respective outputs, 5%, 4% and 2% are defective. A bolt is drawn at random from the total production and it is found to be defective. Find the probability that it was manufactured by machine C.
A committee of 4 persons has to be chosen from 8 boys and 6 girls, consisting of at least one girl. Find the probability that the committee consists of more girls than boys.
In an automobile factory, certain parts are to be fixed into the chassis in a section before it moves into another section. On a given day, one of the three persons A, B, and C carries out this task. A has a 45% chance, B has a 35% chance and C has a 20% chance of doing the task.
The probability that A, B, and C will take more than the allotted time is `(1)/(6), (1)/(10), and (1)/(20)` respectively. If it is found that the time taken is more than the allotted time, what is the probability that A has done the task?
State the sample space and n(S) for the following random experiment.
A coin is tossed twice. If a second throw results in head, a die thrown, otherwise a coin is tossed.
A coin and a die are tossed. State sample space of following event.
B: Getting a prime number.
Find total number of distinct possible outcomes n(S) of the following random experiment.
From a box containing 25 lottery tickets any 3 tickets are drawn at random.
Find total number of distinct possible outcomes n(S) of the following random experiment.
6 students are arranged in a row for a photograph.
Two dice are thrown. Write favourable outcomes for the following event.
R: Sum of the numbers on two dice is a prime number.
Also, check whether Events P and Q are mutually exclusive and exhaustive.
Two dice are thrown. Write favourable outcomes for the following event.
R: Sum of the numbers on two dice is a prime number.
Also, check whether Events Q and R are mutually exclusive and exhaustive.
A card is drawn at random from an ordinary pack of 52 playing cards. State the number of elements in the sample space if consideration of suits is taken into account.
There are 2 red and 3 black balls in a bag. 3 balls are taken out at random from the bag. Find the probability of getting 2 red and 1 black ball or 1 red and 2 black balls.
A bag contains 4 white and 5 black balls. Another bag contains 9 white and 7 black balls. A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag. Find the probability that the ball drawn is white.
Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are kings?
A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
Ten coins are tossed. What is the probability of getting at least 8 heads?
A lot of 100 watches is known to have 10 defective watches. If 8 watches are selected (one by one with replacement) at random, what is the probability that there will be at least one defective watch?
A die is thrown three times. Let X be ‘the number of twos seen’. Find the expectation of X.
An urn contains m white and n black balls. A ball is drawn at random and is put back into the urn along with k additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Show that the probability of drawing a white ball now does not depend on k.
Three bags contain a number of red and white balls as follows:
Bag 1:3 red balls, Bag 2:2 red balls and 1 white ball
Bag 3:3 white balls.
The probability that bag i will be chosen and a ball is selected from it is `"i"/6`, i = 1, 2, 3. What is the probability that a red ball will be selected?
There are three urns containing 2 white and 3 black balls, 3 white and 2 black balls, and 4 white and 1 black balls, respectively. There is an equal probability of each urn being chosen. A ball is drawn at random from the chosen urn and it is found to be white. Find the probability that the ball drawn was from the second urn.
A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement the probability of getting exactly one red ball is ______.
Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl is ______.
A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number on the die and a spade card is ______.
A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is ______.
A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are dead is ______.
Eight coins are tossed together. The probability of getting exactly 3 heads is ______.
In a college, 30% students fail in physics, 25% fail in mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in physics if she has failed in mathematics is ______.
A and B are two students. Their chances of solving a problem correctly are `1/3` and `1/4`, respectively. If the probability of their making a common error is, `1/20` and they obtain the same answer, then the probability of their answer to be correct is ______.
A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?
A card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either ace or a king?
Three horses A, B, Care in a race. A is twice as likely to win as B, and B is twice as likely to win as C. The probability that C wins, P(C) is
A box contains 10 balls, of which 3 are red, 2 are yellow, and 5 are blue. Five balls are randomly selected with replacement. Calculate the probability that fewer than 2 of the selected balls are red?
A bag contains 10 white and 3 black balls. Balls are drawn without replacement till all the black balls are drawn. What is the probability that this procedure will come to an end on the seventh draw?
There are three machines and 2 of them are faulty. They are tested one by one in a random order till both the faulty machines are identified. What is the probability that only two tests are needed to identify the faulty machines?
