Advertisements
Advertisements
Question
A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
Solution
Here, p = `1/6 + 1/6 + 1/6 = 1/2`
q = `1 - 1/2 = 1/2`
And n = 5
∴ P(x = r) = `""^"n""C"_"r" "p"^"r" "q"^("n" - "r")`
= `""^5"C"_3 (1/3)^3 (1/2)^(5-3)`
= `(5!)/(3!2!) * (1/2)^3 * (1/2)^2`
= `10*1/8*1/4`
= `5/16`
Hence, the required probability is `5/16`.
APPEARS IN
RELATED QUESTIONS
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 of getting at least 3 heads?
A fair coin is tossed 8 times, find the probability of exactly 5 heads .
A coin is tossed 5 times. What is the probability that head appears an even number of times?
In a bag, there are three balls; one black, one red, and one green. Two balls are drawn one after another with replacement. State sample space and n(S).
A coin and a die are tossed. State sample space of following event.
A: Getting a head and an even number.
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.
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.
Consider an experiment of drawing two cards at random from a bag containing 4 cards marked 5, 6, 7, and 8. Find the sample Space if cards are drawn without replacement.
Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag and a ball is selected at random. Determine the probability of selecting a black ball.
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?
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?
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 die is thrown three times. Let X be ‘the number of twos seen’. Find the expectation of X.
Two natural numbers r, s are drawn one at a time, without replacement from the set S = {1, 2, 3, ...., n}. Find P[r ≤ p|s ≤ p], where p ∈ S.
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.
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 white ball is selected?
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.
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 ______.
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 ______.
Two cards are drawn at random from a pack of 52 cards one-by-one without replacement. What is the probability of getting first card red and second card Jack?
Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is?
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?
