From noon until sunset, bees emerge from a beehive according to a Poisson proces

Question

From noon until sunset, bees emerge from a beehive according to a Poisson process with rate =2per second.
Find the probability that bees 1 and 2 emerge less than 0.35 seconds apart while bees 3 and 4 emerge more than 0.35 seconds apart.  

(I know this answer, 0.249988)

Find the probability that bees 5 and 6 emerge less than 0.35 seconds apart while bees 7 and 10 emerge more than 0.35 seconds apart.  
Find the probability that the 2nd bee emerges less than 0.97 seconds after noon and the 4rd bee emerges more than 0.97 seconds after noon. (Hint: Are the events independent?)

I posted this question 3times, and I still haven't got the right answer. So, if the answer you got for 1 is not correct, please don't answer to this question...

Explanation / Answer

1)probability that bees 1 and 2 emerge less than 0.35 seconds apart while bees 3 and 4 emerge more than 0.35 seconds apart. =(1-e-t1)*e-t2   where t1 =0.35=t2

=(1-e-0.35*2)*e-0.35*2 =0.249988

2) here first process is exponential withP(X<=0.35) and second is poisson with P(X<=2)

probability that bees 5 and 6 emerge less than 0.35 seconds apart while bees 7 and 10 emerge more than 0.35 seconds apart =(1-e-0.35*2)*(e-t*( t)0/0!+e-t*( t)1/1!+e-t*( t)2/2!) =0.486227

3)robability that the 2nd bee emerges less than 0.97 seconds after noon and the 4rd bee emerges more than 0.97 seconds after noon. =P(2<=X<=3) =0.445295

please revert

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