## Mimi_x3 3 years ago Probability: A man is restoring ten old cars, six of them manufactured in $$1955$$ and four of them manufactured in $$1962$$. When he tries to start them, on average the $$1955$$ models will start $$65$$ percent of the time and the 1962 models will start $$80$$ percent of time. Find the probability that any time: a) exactly three of the $$1955$$ models and one of the $$1962$$ model will start.

1. Mimi_x3

This is what I got but i dont know why its not right.. $\tbinom{6}{3} *(0.39)^3+(0.61)^3 + \binom{4}{1} *(0.39)^1*(0.61)^3$

2. apoorvk

Okay yes, so why did you multiply those factorials - He does not have to 'choose' cars - the cars that start up could be any three outta the 6! And also, you multiply together the probabilities for both kinds of cars - since in the end you want 4 cars to start and 6 not to (with their own respective probabilities governing their 'fates'). (and I believe you wanted to 'multiply' the cube of 0.61 over there, and meant '0.20' and '0.80' for the 1962 models)

3. Mimi_x3

This is called Binomial Probability related to the Binomial Expansion..

4. apoorvk

So your expression should be: $\large (0.61)^3\times (0.39)^3 \times (0.80) \times (0.20)^3$

5. apoorvk

Yeah I was guessing this was something like Binomial - but I don't know what use multiply the 'combinations' would be in this particular case.

6. Mimi_x3

7. Mimi_x3

the binomial expansion: $(a+b)^n = \binom{n}{r} *(a)^{n-r} * (b)^{n}$

8. apoorvk

Anyways, just correct the 'multiplication' sign in your equation and the '0.80' values, and see if that gets you the answer... I am still wondering..

9. Mimi_x3

nope..

10. Mimi_x3

$\binom{6}{3} *(0.61)^3*(0.39)+\binom{4}{1} *(0.80)^1*(0.20)^3$ apparently not right

11. apoorvk

you obviously need to multiply the two probabilities, not add them - think about it.

12. Mimi_x3

still not right

13. Mimi_x3

close though

14. Mimi_x3

the answer is $$0.0060$$

15. apoorvk

and what do you seem to be getting?

16. Mimi_x3

$$0.0453$$ man i hate probability; forget it

17. apoorvk

I am starting to hate it too -...-

18. Mimi_x3

lol its horrible; too confusing -_-