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Two identical cameras, call them A and B, have their flashes fail 21% and 23% of the time respectively. A photographer selects a camera at

Two identical cameras, call them A and B, have their flashes fail 21% and 23% of the time respectively. A photographer selects a camera at random and uses it to take 10 shots with the flash. What is the probability that the flash failed exactly twice?

My solution is 1/2(10C2 * (0.23^2 * 0.77^8 + 0.21^2 * 0.79^8)) = 0/2976. Am I correct?

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