EduNinjaA 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 Var(X).
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).
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.
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.
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.
An ordinary fair die is thrown repeatedly until a 1 or a 6 is obtained.
Find the probability that it takes at least 3 throws but no more than 5 throws to obtain a 1 or a 6 .
On another occasion, this die is thrown 3 times. The random variable X is the number of times that a 1 or a 6 is obtained.
Draw up the probability distribution table for X.
Find E(X).
An ordinary fair die is thrown until a 6 is obtained.
Find the probability that obtaining a 6 takes more than 8 throws. Two ordinary fair dice are thrown together until a pair of 6s is obtained.
The number of throws taken is denoted by the random variable X.
Find the expected value of X.
Find the probability that obtaining a pair of 6s takes either 10 or 11 throws.
In a certain large college, 22 % of students own a car.
3 students from the college are chosen at random. Find the probability that all 3 students own a car.
16 students from the college are chosen at random. Find the probability that the number of these students who own a car is at least 2 and at most 4 .
A bag contains 5 red balls and 3 blue balls. Sadie takes 3 balls at random from the bag, without replacement. The random variable X represents the number of red balls that she takes.
Draw up the probability distribution table for X.
Given that E(X)=815, find Var(X).
In a certain country, the probability of more than 10 cm of rain on any particular day is 0.18 , independently of the weather on any other day.
Find the probability that in any randomly chosen 7-day period, more than 2 days have more than 10 cm of rain.
For 3 randomly chosen 7-day periods, find the probability that exactly two of these periods have at least one day with more than 10 cm of rain.