Given that $X~Geo\left(p\right)$ and that $P\left(X\le 4\right)=\frac{2385}{2401}$, find $P\left(1\le X<4\right).$

Important Questions on The Binomial and Geometric Distributions

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7C>Q 15

Two ordinary fair dice are rolled simultaneously. Find the probability of obtaining: the first double on the fourth roll.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7C>Q 15

Two ordinary fair dice are rolled simultaneously. Find the probability of obtaining: the first pair of numbers with a sum of more than $10$ before the $10$ th roll.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7C>Q 16

$X~Geo\left(0.24\right)$ and $Y~Geo\left(0.25\right)$ are two independent random variables. Find the probability that $X+Y=4.$

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7D>Q 1

Given that $X~Geo\left(0.36\right)$, find the exact value of $E\left(X\right)$.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7D>Q 2

The random variable $Y$ follows a geometric distribution. Given that $P\left(Y=1\right)=0.2$, find $E\left(Y\right)$.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7D>Q 3

Given that $S~Geo\left(p\right)$ and that $E\left(S\right)=4\frac{1}{2}$, find $P\left(S=2\right).$

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7D>Q 4

Let $T$ be the number of times that a fair coin is tossed, up to and including the toss on which the first tail is obtained. Find the mode and the mean of $T$.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7D>Q 5

Let $X$ be the number of times an ordinary fair die is rolled, up to and including the roll on which the first $6$ is obtained. Find $E\left(X\right)$ and evaluate $P\left[X>E\left(X\right)\right]$.