How to solve this?There are three events A,B,C one of which must and only one can happen.The odds are 7 to 3 against A and 6 to 4 against B,find the odds against C

I cant understand what to take as the favourable event and total event.And how to solve this

Answer 1

The odds for C are the same as A, or 7 to 3 against.

Notice that for events A and B, we're looking at 10 events in total for both (7 to 3, 6 to 4).

Also notice that we're talking about the odds against the events happening out of 10 tries. A won't happen 7 out of 10 times (which means it will happen 3 out of 10 times). And for B, it won't happen 6 out of 10 times (which means it will happen 4 out of 10 times).

And so out of 10 times, A happen 3 times and B happens 4 times. That leaves 3 times that C can happen (and, in fact, must happen since one and only one event must occur).

And so the odds for C are the same as A, or 7 to 3 against.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the odds against event C, you can use the fact that the sum of the probabilities of all possible outcomes must equal 1.

First, calculate the probabilities of events A and B occurring:

  • Probability of event A = 3 / (7 + 3) = 3/10
  • Probability of event B = 4 / (6 + 4) = 4/10

Since only one event can occur, the probability of event C is 1 minus the sum of the probabilities of events A and B:

  • Probability of event C = 1 - (3/10 + 4/10) = 1 - 7/10 = 3/10

Now, to find the odds against event C, you can use the ratio of the probability of event C not happening to the probability of it happening:

  • Odds against event C = (Probability of C not happening) : (Probability of C happening) = (7/10) : (3/10)

Thus, the odds against event C are 7 to 3.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7