Suppose that A and B are two events in a sample space, S, which are independent and which have equal probability, p, of occurrin
1 answer:
Answer:
The probability that both A and B occur is P = 0.01
Step-by-step explanation:
Both events A and B have a probability p of occurring.
Then both events A and B have a probability (1 - p) of NOT occurring.
The probability that neither A or B occurs is equal to the product of the individual probabilities, and this is equal to 0.81, then:
(1 - p)*(1 - p) = 0.81
1 - 2*p + p^2 = 0.81
p^2 - 2*p + 0.19 = 0
We can solve this if we use Bhaskara's equation, the two solutions are:
Then the two solutions are:
p = (2 + 1.8)/2 = 3.8/2 = 1.9
A probability must be a number between zero and one, and this is larger than one, so this solution can be discarded.
the other solution is:
p = (2 - 1.8)/2 = 0.2/2 = 0.1
This means that the probability that event A occurs is p = 0.1
And the probability that event B occurs is p = 0.1
The probability that both events occur is equal to the product of the individual probabilities, which is:
P = 0.1*0.1 = 0.01
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