ryanwortham6
ryanwortham6 ryanwortham6
  • 23-01-2019
  • Mathematics
contestada

Two events, A and B, are disjoint. What is the probability that both A and B will occur at the same time?

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kudzordzifrancis
kudzordzifrancis kudzordzifrancis
  • 23-01-2019
ANSWER

[tex]P(A\cap B)=0[/tex]

EXPLANATION

If the two events are disjoint, then they are mutually exclusive.

This means that their intersection is zero.

Therefore

[tex]n(A\cap B)=0[/tex]

This implies that,

[tex]P(A\cap B)= \frac{n(A\cap B)}{n(U)} [/tex]

[tex]P(A\cap B)= \frac{0}{n(U)} = 0[/tex]

The probability that the two events will occur together is 0, which means an impossibility.
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