Question

[15 points] It is known that 30% of the rocket launchings at a NASA base have to be delayed 3 to weaher conditions. What is the probability that among 10 rocket launchings at that base (a). Exactly 3 will be delayed due to weather? (b). At most 6 will be delayed due to weather?

Answer 1

p = 0.30 , n =10

As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

a)
P(x =3) = 10C3 * 0.30^3 * (1-0.30)^7

= 0.2668

b)
P(x <=6) = P(x =0) + P(x =1) + P(x =2) + P(x =3) + P(x =4) + P(x =5) + P(x =6)

= 10C0 * 0.30^0 * (1-0.30)^10 + 10C1 * 0.30^1 * (1-0.30)^9 + 10C2 * 0.30^2 * (1-0.30)^8 + 10C3 * 0.30^3 * (1-0.30)^7 + 10C4 * 0.30^4 * (1-0.30)^6 + 10C5 * 0.30^5 * (1-0.30)^5 + 10C6 * 0.30^6 * (1-0.30)^4

= 0.9894