Question

Problem 4. A fair coin is tossed consecutively 3 times. Find the conditional probability P(A | B), where the events A and B are defined as A-(more heads than tails came upl, B-(1st toss is a head) 1St toss is a head Problem 5. Consider rolling a pair of dice once. What is the probability of getting 7, given that the sum of the faces is an odd number?

Answer 1

4) $A=\left \{ (H,H,T),(H,T,H),(T,H,H) \right \}$

and $B=\left \{ (H,H,H)(H,H,T),(H,T,H),(H,T,T) \right \}$

$A\cap B=\left \{ (H,H,T),(H,T,H) \right \}$

$P(A|B)=\frac{n(A\cap B)}{n(B)}=\frac{2}{4}=\frac{1}{2}=0.5$

5)

Sum	2	3	4	5	6	7	8	9	10	11	12
Probability	$\frac{1}{36}$	$\frac{2}{36}$	$\frac{3}{36}$	$\frac{4}{36}$	$\frac{5}{36}$	$\frac{6}{36}$	$\frac{5}{36}$	$\frac{4}{36}$	$\frac{3}{36}$	$\frac{2}{36}$	$\frac{1}{36}$

The probability of getting 7 and the sum of the faces is odd number is $\frac{6}{36}$

The probability of getting odd number is $\frac{2+4+6+4+2}{36}=\frac{18}{36}$

Required probability = $\frac{\frac{6}{36}}{\frac{18}{36}}=\frac{6}{18}=\frac{1}{3}=0.3333$