EduNinjaThe numbers on the faces of a fair six-sided dice are 1,2,2,3,3,3. The random variable X is the total score when the dice is rolled twice.
Draw up the probability distribution table for X.
Find the value of .
The random variable X takes the values -2,2 and 3. It is given that
where k is a constant.
Draw up the probability distribution table for X, giving the probabilities as numerical fractions.
Find E(X) and .
A fair red spinner has edges numbered 1,2,2,3. A fair blue spinner has edges numbered -3,-2,-1,-1. Each spinner is spun once and the number on the edge on which each spinner lands is noted. The random variable X denotes the sum of the resulting two numbers.
Draw up the probability distribution table for X.
Given that E(X)=0.25, find the value of .
Two fair coins are thrown at the same time repeatedly until a pair of heads is obtained. The number of throws taken is denoted by the random variable X.
State the value of E(X).
Find the probability that exactly 5 throws are required to obtain a pair of heads.
Find the probability that fewer than 7 throws are required to obtain a pair of heads.
The score when two fair six-sided dice are thrown is the sum of the two numbers on the upper faces.
The two dice are thrown repeatedly until a score of 4 is obtained. The number of throws taken is denoted by the random variable X.
Find the mean of X.
Find the probability that a score of 4 is first obtained on the 6th throw.
Find P(X<8).
Two fair coins are thrown at the same time. The random variable X is the number of throws of the two coins required to obtain two tails at the same time.
Find the probability that two tails are obtained for the first time on the 7th throw.
Find the probability that it takes more than 9 throws to obtain two tails for the first time.
A competitor in a throwing event has three attempts to throw a ball as far as possible. The random variable X denotes the number of throws that exceed 30 metres. The probability distribution table for X is shown below.
Given that E(X)=1.1, find the value of p and the value of r.
Find the numerical value of .
An ordinary fair die is thrown repeatedly until a 5 is obtained. The number of throws taken is denoted by the random variable X.
Write down the mean of X.
Find the probability that a 5 is first obtained after the 3rd throw but before the 8th throw.
Find the probability that a 5 is first obtained in fewer than 10 throws.
Rajesh applies once every year for a ticket to a music festival. The probability that he is successful in any particular year is 0.3 , independently of other years.
Find the probability that Rajesh is successful for the first time on his 7th attempt.
Find the probability that Rajesh is successful for the first time before his 6th attempt.
Find the probability that Rajesh is successful for the second time on his 10th attempt.
A fair six-sided die, with faces marked 1,2,3,4,5,6, is thrown repeatedly until a 4 is obtained.
Find the probability that obtaining a 4 requires fewer than 6 throws.
On another occasion, the die is thrown 10 times.
Find the probability that a 4 is obtained at least 3 times.