Here are the probabilities of two independent events.
Event A 2.7 × 10–2 Event B 3.4 × 10–4
Work out the probability of only one of the events happening.
Give your answer to 3 significant figures.
The probability that A occurs = 0.027
The probability that B occurs = 0.00034
The probability that A doesn't occur = 1.000 - 0.027 = 0.973
The probability that B doesn't occur = 1.00000 - 0.00034 = 0.99966
The probability that only one of these independent occurs
= ( probability that A occurs and B doesn't occur )
+ ( probability that B occurs and A doesn't occur )
The probability that A occurs and B doesn't occur = 0.027 x 0.99966 = 0.02699082
The probability that B occurs and A doesn't occur = 0.00034 x 0.973 = 0.00033082
Adding these two values together = 0.0273 (rounded to 3 significant digits)