The probability for event a is 0.3, the probability for event b is 0.5, and the probability of events a and b is 0.25. are the events independent?

The probability for event A is 0.3, the probability for event B is 0.5, and the probability of events A and B is 0.25. No, they are not independent events.

The probability of an event is the possibility or likelihood for the event to occur.

In probability, an independent event has no impact and doesn't depend on the probability of another event taking place.

If the probability of event i.e.

Then,  if these events are independent, the intersection of P(A) and P(B) must be equal to P(A ∩ B).

P(A) and P(B)  ≠  P(A ∩ B), Hence, they are not independent events.

Therefore, we can conclude that the event of A (0.3) and event of B(0.5) are independent events to P(A ∩ B)

Learn more about independent events here;

link

For this case we have to:

Two or more events are independent when the occurrence or non-occurrence of one event has no effect on the probability of occurrence of the other event.

By definition, A is independent of B if and only if:

(P∩B) = P (A) P (B)

We have to:

So:

According to the statement

So, the events are not independent!

They are not independent!

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

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