AP EAMCET202316 May 2023Morning ShiftMathematicsProbabilityActual
In a city it is found that 10 accidents took place in a span of 50 days. Assuming that the number of accidents follow the Poisson distribution, the probability that there will be 3 or more accidents in a day in that city is
Options
- A1-(1.02) e ^ 0.2
- B1-(1.22) e ^ -0.2
- C1-(1.2) e ^ 0.2
- D1- 1.22 e ^ -0.2
Correct answer
C. 1-(1.2) e ^ 0.2
Step-by-step solution
X poisson ( ) Mean ( )= 10 50 = 1 5 P(X 3)=1-P(X=0)-P(X=1)-P(X=2) aligned & =1- e^ - ^0 0 ! - e^ - ^1 1 ! - e^ - ^2 2 ! & =1-e^ - 1 5 [ ( 1 5 )^0+ ( 1 5 )+ 1 2 ( 1 25 ) ] & =1-e^ - 1 5 [1+ 1 5 + 1 50 ] & =1-e^ -0.2 [ 61 50 ]=1-e^ -0.2 1.22 & P(X 3)=1-1.22 e^ -0.2 aligned