# Math Help - conditional probablity

1. ## conditional probablity

Hi everyone,

Given:
Coin tossing
A balanced dime is tossed twice. The four possible equaly likely outcomes are HH,HT, TH, TT

Let:

A=event the first toss is heads
B=event the second toss is heads
C=event at least one toss is heads

Determine the following probabilities and express your results in words. Compute the conditional probabilities directly; do not use the conditional probability rule

a. P(B)

Would it be 3/4???????

b. P(B|A)

Would it be 1/3????????

c. P(B|C)

Would this also be 1/3???????

d. P(c)

1/3????

e. P(C|A)

f. P(|not B))

I really don't understand this. Could someone please explain this to me so that I can do the rest that are like this?

any help would be greatly appreciated

Thank you very much

2. For a)

The possibilities are HH, HT, TH, TT

so the probability that the second toss is heads is 2 out of the four possibilities. It makes sense because HT and TT are the only two that satisfy this condition. Therefore, 1/2

3. For d)

3 out of the four possibilities have a H in them HT, TH, HH

4. Thank you very much

I understand "d" now, but I still don't understand "a".

For a)

The possibilities are HH, HT, TH, TT

so the probability that the second toss is heads is 2 out of the four possibilities. It makes sense because HT and TT are the only two that satisfy this condition. Therefore, 1/2
How do you know that "HH" and "TT" are the only two that satisfy this condition? Wouldn't it be "HH" "HT" and "TH"? because they are the ones that have a "heads"

Thank you