- #1
Pushoam
- 962
- 51
Homework Statement
Homework Equations
The Attempt at a Solution
12)a)
a) Since both events are independent : P( 33) = 9 / 441
b) Let’s have
4: throwing 4
Not 4 : not throwing 4
P ( 4 and not throwing 4 ) = P( 4) P ( not throwing 4) = (17*4)/441c) Let’s consider the sample event S for the above problem:
S : {(6,4),(4,6),(5,6),(6,5),(5,5),(6,6)}
Probability of getting 5 and 5 under given condition is : P(55/S)
Using Bayes’ theorem,
P(55/S) = P(55 and S)/ P(S)As S contains (5,5) as a sample point, P(55 and S) = P(55)
Is it always true that P (A and B) = P (A),when A is a subset of B ?P(55/S) = ## \frac { \frac {5 *5 } {21*21 } } {(2*6*4 +2*5*6 +25+36)/441 } ##
= ## \frac { 25 } { 169 } ##d) I think what the question says is:
I throw the dice n times, what is the probability that I will get an ace once?
The dice throwing n times and getting an ace once is equivalent to that I have n boxes and I have to put one ace in any of these n boxes. The probability of getting an ace is 1/21 in one throw. So, the probability of getting one ace in n throws is n/21.Now, ## \frac { n } {21 } \geq ½
\\ n \geq 11 ##
e) S = {(2,5),(2,6), (4,5),(4,6), (6,5),(6,6)}
P(S) = 132/441
Is this correct ?