Advertisements
Advertisements
Question
A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire in order to have more than 50% chance of hitting it at least once is
Options
11
9
7
5
Solution
7
Let p=chance of hitting a distant target
\[\Rightarrow\] p =10% or p= 0.1
\[\Rightarrow q = 1 - 0 . 1 = 0 . 9\]
\[\text{ Let n be the least number of rounds } . \]
\[P(\text{ hitting atleast once} ) = P(X \geq 1) \]
\[ \Rightarrow 1 - P(X = 0) \geq 50 \% \]
\[ \Rightarrow 1 - P(X = 0) \geq 0 . 5\]
\[P(X = 0) \leq 0 . 5\]
\[ \Rightarrow (0 . 9 )^n \leq 0 . 5\]
\[\text{ Taking } \text{ log on both the sides, we get} \]
\[ n \text{ log } 0 . 9 \leq \log 0 . 5 \]
\[ \Rightarrow n \leq \frac{\log 0 . 5}{\log 0 . 9}\]
\[ \Rightarrow n \leq 7 . 2 \]
\[\text{ Therefore, 7 is the least number of rounds that he must fire in order } \]
\[ \text{ to have more than 50 % chance of hitting the target at least once } . \]
APPEARS IN
RELATED QUESTIONS
A fair coin is tossed 8 times. Find the probability that it shows heads at least once
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that
- all the five cards are spades?
- only 3 cards are spades?
- none is a spade?
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one, will fuse after 150 days of use.
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100. What is the probability that he will in a prize (a) at least once (b) exactly once (c) at least twice?
A couple has two children, Find the probability that both children are females, if it is known that the elder child is a female.
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.
Five cards are drawn one by one, with replacement, from a well-shuffled deck of 52 cards. Find the probability that
(i) all the five cards diamonds
(ii) only 3 cards are diamonds
(iii) none is a diamond
A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that none is white ?
A card is drawn and replaced in an ordinary pack of 52 cards. How many times must a card be drawn so that (i) there is at least an even chance of drawing a heart (ii) the probability of drawing a heart is greater than 3/4?
The mathematics department has 8 graduate assistants who are assigned to the same office. Each assistant is just as likely to study at home as in office. How many desks must there be in the office so that each assistant has a desk at least 90% of the time?
The probability that a certain kind of component will survive a given shock test is \[\frac{3}{4} .\] Find the probability that among 5 components tested at most 3 will survive .
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is `1/100`. What is the probability that he will win a prize at least once.
Find the probability that in 10 throws of a fair die, a score which is a multiple of 3 will be obtained in at least 8 of the throws.
A factory produces bulbs. The probability that one bulb is defective is \[\frac{1}{50}\] and they are packed in boxes of 10. From a single box, find the probability that exactly two bulbs are defective
A factory produces bulbs. The probability that one bulb is defective is \[\frac{1}{50}\] and they are packed in boxes of 10. From a single box, find the probability that more than 8 bulbs work properly
A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.
In eight throws of a die, 5 or 6 is considered a success. Find the mean number of successes and the standard deviation.
A dice is thrown thrice. A success is 1 or 6 in a throw. Find the mean and variance of the number of successes.
In a binomial distribution, if n = 20 and q = 0.75, then write its mean.
If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.
If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X = 4) in terms of α.
An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
A fair coin is tossed 100 times. The probability of getting tails an odd number of times is
A biased coin with probability p, 0 < p < 1, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is 2/5, then p equals
Mark the correct alternative in the following question:
The probability of guessing correctly at least 8 out of 10 answers of a true false type examination is
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that none is a spade ?
For Bernoulli Distribution, state formula for E(X) and V(X).
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If P(x = r)/P(x = n – r) is independent of n and r, then p equals ______.
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9, P(X = 3), then p = ______.
The sum of n terms of the series `1 + 2(1 + 1/n) + 3(1 + 1/n)^2 + ...` is
If x4 occurs in the tth term in the expansion of `(x^4 + 1/x^3)^15`, then the value oft is equal to:
If in the binomial expansion of (1 + x)n where n is a natural number, the coefficients of the 5th, 6th and 7th terms are in A.P., then n is equal to:
If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then `(P(X = 2))/(P(X = 3))` is equal to ______.
