# Thread: Probability with a die and with coins.

1. ## Probability with a die and with coins.

Hello Everyone
How r u doing?

hmmm this is my homework, I've solved part of it but i faced some difficulties with the rest Qs.

Prob. 1:
Let A and B be two events. Prove the following:
*P(A intercept B)>= P(A)+P(B)-1
*P(AUnion b)>=P(A)
Prob. 2:
A die is loaded in such a way that the probability of each face turning up is proportional to the number of dots on that face. (For example, a six is three times as probable as a two.) . The die is thrown once.
• What is the probability of getting 1?
• What is the probability of getting an odd number?
Prob. 3:
You have 2 coins, a fair one with P(H) = ½, and an unfair one with P(H) = 1/3. A coin is selected at random and tossed, falling heads up. How likely that it is the fair one?

Many thanx

2. Originally Posted by my.life
Hello Everyone
How r u doing?

hmmm this is my homework, I've solved part of it but i faced some difficulties with the rest Qs.

Prob. 1:
Let A and B be two events. Prove the following:
*P(A intercept B)>= P(A)+P(B)-1
*P(AUnion b)>=P(A)
Prob. 2:

A die is loaded in such a way that the probability of each face turning up is proportional to the number of dots on that face. (For example, a six is three times as probable as a two.) . The die is thrown once.

• What is the probability of getting 1?
• What is the probability of getting an odd number?
Prob. 3:
You have 2 coins, a fair one with P(H) = ½, and an unfair one with P(H) = 1/3. A coin is selected at random and tossed, falling heads up. How likely that it is the fair one?

Many thanx
1) Draw a Venn diagram to assist in the proof.

2) Write out the probability distribution table:

Pr(X = 1) = k
Pr(X = 2) = 2k
Pr(X = 3) = 3k
.
.
.
Pr(X = 6) = 6k.

1 = k + 2k + 3k + .... + 6k => k =

Now that you know the probabilities you can answer the questions.

3) Start by drawing a tree diagram. Can you do this?