Question

IF P(A OR B) = 0.9, P(A) = 0.5, AND P(B) = 0.6, FIND P(A AND B)

Answer 1

Answer:

$P(A\ and\ B) = 0.2$

Step-by-step explanation:

The probability of either A or B occurring can be defined as:

$P(A\ or\ B) = P(A) + P(B) - P(A\ and\ B)$

The reason for subtracting the P(A and B), is because you don't want to count the probability twice.

So I attached an image which displays this. If we wanted to calculate the probability of a red or circle object. we could just count all the objects in both circles, and add them up and divide it by the entire amount

So there is 12 shapes in total, inside the two circles, and since there are 10 other objects also, which don't fit either conditions, the probability of choosing either is: $\frac{12}{12+10}=\frac{12}{22}=\frac{6}{11}$

What if we just added the two probabilities though? Well there's 9 red objects, and 6 circles, so the probability would be: $\frac{9}{22} + \frac{6}{22} = \frac{15}{22}$

That looks higher than the 12/22 which we had before simplifying. The reason for this, is because there is some overlap in red objects and shapes that are circles. For this reason, we must subtract this overlap, since it's already being counted in one of the probabilities.

For example when I calculate the probability of a circle, it contains 3 red objects.

Now if I calculate the probability of a red object, the overlap is those 3 red circles, but we already counted it in the other probability, so to remove this overlap we simply subtract, and now we have the actual probability.

Let's look back at when we added the probabilities and got 15/22, since there is 3 shapes that are circles and red, had we subtracted it, we would've got (15-3)/22 which is 12/22. This is the actual probability which we got initially.

So this means that:

$P(A\ or\ B) = P(A) +P(B)-P(A\ and\ B)$

Filling in known values we get:

$0.9 = 0.5+0.6-P(A\ and\ B)$

Add values

$0.9 = 1.1 - P(A\ and\ B)$

Subtract 1.1 from both sides

$-0.2 = -P(A\ and\ B)$

Multiply or divide both sides by -1

$0.2 = P(A\ and\ B)$

Answer 2

Answer:

The answer is = 0.3

Step-by-step explanation:

To find p( A and B)

P(A) × P(B)

= 0.5 × 0.6

= 0.3

MARK BRAINLIEST