Advertisements
Advertisements
प्रश्न
A fair coin is tossed 8 times, find the probability of at most 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 \[q = 1 - \frac{1}{2} = \frac{1}{2}\]
Probability of getting at most 6 heads
\[= P\left( X \leq 6 \right)\]
\[ = 1 - \left[ P\left( X = 7 \right) + P\left( X = 8 \right) \right]\]
\[ = 1 - \left[ {}^8 C_7 \left( \frac{1}{2} \right)^8 +^8 C_8 \left( \frac{1}{2} \right)^8 \right]\]
\[ = 1 - \left( \frac{8}{256} + \frac{1}{256} \right)\]
\[ = 1 - \frac{9}{256}\]
\[ = \frac{247}{256}\]
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.
A coin is tossed 5 times. What is the probability that tail appears an odd number of times?
A fair coin is tossed 8 times, find the probability of exactly 5 heads .
A fair coin is tossed 8 times, find the probability of at least six heads
A pair of dice is thrown. What is the probability of getting an even number on the first die or a total of 8?
One dialing certain telephone numbers assume that on an average, one telephone number out of five is busy, Ten telephone numbers are randomly selected and dialed. Find the probability that at least three of them will be busy.
State the sample space and n(S) for the following random experiment.
A coin is tossed twice. If a second throw results in a tail, a die is thrown.
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.
C: Getting a tail and perfect square.
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.
From a group of 4 boys and 3 girls, any two students are selected at random.
Find total number of distinct possible outcomes n(S) of the following random experiment.
5 balls are randomly placed into 5 cells, such that each cell will be occupied.
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.
Box-I contains 8 red (R11, R12, R13) and 2 blue (B11, B12) marbles while Box-II contains 2 red(R21, R22) and 4 blue (B21, B22, B23, B24) marbles. A fair coin is tossed. If the coin turns up heads, a marble is chosen from Box-I; if it turns up tails, a marble is chosen from Box-II. Describe the sample space.
A car manufacturing factory has two plants, X and Y. Plant X manufactures 70% of cars and plant Y manufactures 30%. 80% of the cars at plant X and 90% of the cars at plant Y are rated of standard quality. A car is chosen at random and is found to be of standard quality. What is the probability that it has come from plant X?
A bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one without replacement. What is the probability that at least one of the three marbles drawn be black, if the first marble is red?
Prove that P(A) = `"P"("A" ∩ "B") + "P"("A" ∩ bar"B")`
A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also not noted. Then another ball is drawn at random. What is the probability of second ball being blue?
Ten coins are tossed. What is the probability of getting at least 8 heads?
The probability of a man hitting a target is 0.25. He shoots 7 times. What is the probability of his hitting at least twice?
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 and B throw a pair of dice alternately. A wins the game if he gets a total of 6 and B wins if she gets a total of 7. It A starts the game, find the probability of winning the game by A in third throw of the pair of dice.
There are two bags, one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls. A die is thrown. If it shows up 1 or 3, a ball is taken from the Ist bag; but it shows up any other number, a ball is chosen from the second bag. Find the probability of choosing a black ball.
By examining the chest X ray, the probability that TB is detected when a person is actually suffering is 0.99. The probability of an healthy person diagnosed to have TB is 0.001. In a certain city, 1 in 1000 people suffers from TB. A person is selected at random and is diagnosed to have TB. What is the probability that he actually has TB?
A bag contains (2n + 1) coins. It is known that n of these coins have a head on both sides where as the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is `31/42`, determine the value of n.
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 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 ______.
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, 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?
The letters of the word "ATTRACTION' are written randomly. The probability that no two T's appear together is
In year 2019, the probability of getting 53 Sundays is
Bag P contains 6 red and 4 blue balls and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q. What is the probability that the ball drawn is blue?
Assertion (A): Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is `1/3`.
Reason (R): Let E and F be two events with a random experiment, then `P(E/F) = (P(E ∩ F))/(P(E))`.
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?
