Starting at time 0, a red bulb flashes according to a Poisson process with rate A = 2. Similarly, starting at time 0, a blue bulb flashes according to a Poisson process with rate A = 1, but only until a nonnegative random time X, at which point the blue bulb "dies!l We assume that the two Poisson processes and the random variable X are {mutually} independent. Suppose that X is equal to either 1 or 2, with equal probability. Write down an expression for the probability that there were exactly 2 arrivals during the time interval [0, 2]. (Enter a for the constant 6. You may use standard notation for this numerical entry even though there will be no parser below the answer box. Enter an exact answer or a numerical answer accurate to at least 3 decimal places.) Probability that there were exactly 2 arrivals during the time interval [0, 2]