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 probability that a score of 4 is first obtained on the 6th throw. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_51 Year：2020 Question No：1(c)

Answer:

$\left(\frac{11}{12}\right)^{5} \times \frac{1}{12}=0.0539$ or $\frac{161051}{2985984}$

Knowledge points:

5.4.2 use formulae for probabilities for the binomial and geometric distributions, and recognise practical situations where these distributions are suitable models (Including the notations B(n,p) and Geo(p). Geo(p) denotes the distribution in which for r = 1,2,3,...)

Answer:

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