Question

You have a set of 10 cards numbered 1 to 10 you choose a card at random event a is choosing a number less than seven is choosing an odd number calculate the following probabilities. B. p(a ∩ b) C.P(B^c)

Answer 1

This problem is about simple probabilities, that is, the ratio between the number of events and the total number of outcomes.

To find the probability of events A and B we need to find first their singles probabilities.

Notice that event A is "choosing a number less than seven". There are 6 numbers less than seven. So, its probability is

`P(A)=(6)/(10)=(3)/(5)`

Then we do the same process to find the probability of "choosing an odd number", we know that there are 5 odd numbers.

`P(B)=(5)/(10)=(1)/(2)`

Now we are able to find the intersection between A and B. Remember, intersection refers to multiplication:

`P(A\cap B)=(1)/(2)\cdot(3)/(5)=(3)/(10)=0.3`

Therefore, the probability of the intersection between A and B is 3/10, or 30%.

On the other hand, we must find the probability of the complement set of B, which is formed by all the numbers not included inside B, that is, 2, 4, 6, 8, and 10. So, this probability would be

`P(B^c)=(5)/(10)=(1)/(2)`

Therefore, the probability of the complement set of B is 1/2, or 50%.