Standard +0.3 This question requires knowing that Poisson distributions sum (λ_total = 0.2+0.3+0.6 = 1.1) and scale with time (4 minutes gives λ = 4.4), then calculating P(X < 4) = P(X ≤ 3) using standard Poisson probability formula. It's a straightforward application of two key Poisson properties with routine calculation, making it slightly easier than average.
1 The numbers of alpha, beta and gamma particles emitted per minute by a certain piece of rock have independent distributions \(\operatorname { Po } ( 0.2 ) , \operatorname { Po } ( 0.3 )\) and \(\operatorname { Po } ( 0.6 )\) respectively. Find the probability that the total number of particles emitted during a 4 -minute period is less than 4.
1 The numbers of alpha, beta and gamma particles emitted per minute by a certain piece of rock have independent distributions $\operatorname { Po } ( 0.2 ) , \operatorname { Po } ( 0.3 )$ and $\operatorname { Po } ( 0.6 )$ respectively. Find the probability that the total number of particles emitted during a 4 -minute period is less than 4.\\
\hfill \mbox{\textit{CAIE S2 2018 Q1 [3]}}