The following table contains the probability distribution for the number of traffic accidents (X) daily in a small town:
No of accidents (X)
0
1
2
3
4
5
P(X)
0.15
0.2
B
0.15
0.15
0.15
Determine:
P(1 X < 4)
P(1≤ X < 4) = P(X = 1) + P(X = 2) + P(X = 3)
P(1≤ X < 4) = 0.2 + B + 0.15
Since the sum of probabilities in a probability distribution should equal 1, we can solve for B by subtracting the sum of known probabilities from 1:
1 = 0.15 + 0.2 + B + 0.15 + 0.15 + 0.15
1 = 0.8 + B
B = 0.2
Now substitute B back into the original equation:
P(1≤ X < 4) = 0.2 + 0.2 + 0.15
P(1≤ X < 4) = 0.55
Therefore, P(1≤ X < 4) = 0.55.