Probability that a chip is operative

[SamTaylor]

Homework Statement

A chip contains twenty identical transistors, which are connected in such a way
that the chip will perform its function provided that no more than three of the
transistors have failed. The probability that any given transistor has failed
equal 0.1. Calculate the probability that the chip is operative.

The Attempt at a Solution

$$\sum_{n=0}^{3}\binom{20}{n} 0.1^{n} (1-0.1)^{20-n}$$

But this can not be right since the probability that the chip is still working
is higher with less transistors but with the same failed number.

20 transistors p = 0.8670
10 transistors p = 0.9872

Can someone give me a hint please.

 

[vela]

I didn't check your calculations, but your approach is correct. Your result is actually reasonable. When you have 20 transistors, there are many more ways to have up to 3 fail than when you have only 10 transistors.