Question

Consider the experiment of flipping 3 coins. Determine the following probabilities:

A) what is the probability that the second coin is heads?

B) what is the probability that the second coin is heads given that either the first coin was tails or the third coin was tails?

Now consider again the experiment of rolling a pair of dice. Determine the following.

A) what is the probability that the first die comes up less than 5?

B) what is the probability that the first die comes up less than 5 given that the second die comes up greater than 4?

Answer 1

a)

probability that the second coin is heads =1/2

b) here as events are independent therefore outcome on second coin will not depend on other flips outcome

probability that the second coin is heads given that either the first coin was tails or the third coin was tails =1/2

2)A) probability that the first die comes up less than 5 =4/6 =2/3 (as out of 6 outcomes ; 4 are less then 5)

B)

here also events are independent therefore probability that the first die comes up less than 5 given that the second die comes up greater than 4 =2/3