Math Help - poisson/Geometric Distribution question????

1. poisson/Geometric Distribution question????

Hi Guys another question, i have not a clue on how to start this question but ill tell you what ive written for it anyway any help for this would be absolutly great!!!

Every packet of TastyBrej contains one of 10 plastic toys, all equally likely, and independantly for each packet. They can be fitted together to make a model space station. Horace has collected 9 toys so far and only need the docking module to complete the space station.
i)
Horaces mother buys packets of Tastybrek according to a poissson process, with a average rate of 1 packet per week.
a) Given that horaces mother buys x packets of tastybrek in 4 weeks, write down the probability that none contains a docking module.
b)State the total law of probabilty and use it to calculate the probabilty that, at the end of the 4 weeks, horace still doesnt have a docking module.

for part ia) i have two answers but theyre both guess
0.9^(x) or e^(-0.4)

ib) I have the total law but am unsure i about the 2nd part i have written. e^(-0.1) x e^(-0.2) x e^(-0.3) x e^(-0.4)= e^(-0.1)

the marks for this is 7marks so i doubt its this easy thank again!!!!

2. Originally Posted by rishul
Hi Guys another question, i have not a clue on how to start this question but ill tell you what ive written for it anyway any help for this would be absolutly great!!!

Every packet of TastyBrej contains one of 10 plastic toys, all equally likely, and independantly for each packet. They can be fitted together to make a model space station. Horace has collected 9 toys so far and only need the docking module to complete the space station.
i)
Horaces mother buys packets of Tastybrek according to a poissson process, with a average rate of 1 packet per week.
a) Given that horaces mother buys x packets of tastybrek in 4 weeks, write down the probability that none contains a docking module.

Mr F says: Pr(no dock | x packets in 4 weeks) ${\color{red}= (0.9)^x}$.

b)State the total law of probabilty and use it to calculate the probabilty that, at the end of the 4 weeks, horace still doesnt have a docking module.

Mr F says: Pr(no dock) = Pr(no dock | x packets in 4 weeks) Pr(x packets in 4 weeks), summed over x = 0 to infinity:

${\color{red} \sum_{x = 0}^{\infty} \left[\Pr(\text{no dock} \, | x \, \text{packets in 4 weeks}) \cdot \Pr(x \, \text{packets in 4 weeks}) \right]}$

Note that ${\color{red}\Pr(x \, \text{packets in 4 weeks}) = \frac{e^{-4} 4^x}{x!}}$.

for part ia) i have two answers but theyre both guess
0.9^(x) or e^(-0.4)

ib) I have the total law but am unsure i about the 2nd part i have written. e^(-0.1) x e^(-0.2) x e^(-0.3) x e^(-0.4)= e^(-0.1)

the marks for this is 7marks so i doubt its this easy thank again!!!!
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