2
votes
1answer
39 views

Coin-tossing games

Suppose that you start off with $100$ dollars. You toss a coin $10$ times and guess it right $5$ times and lose $5$ times (the order of the outcomes is not known). It is known that every time you ...
0
votes
4answers
69 views

Chance of playing a game

You are offered a chance to play a game. the rules are simple. there are $100$ cards face down. Of these, $55$ say win and $45$ say lose. You begin with $10000$ dollars. You must bet $1/2$ of your ...
0
votes
0answers
31 views

Conditional Probability - Order is important!

Probability that Mark wins a tennis match he plays is 0.8. A knockout tournament requires players to win 5 matches to win the tournament. What is the probability that Mark wins the tournament? ...
0
votes
2answers
26 views

Die Probability Question + Basics of Conditional Probability

A die is rolled twice. What is the probability of observing: a) a four and a three P (obtaining a four and a three) or P(obtaining a three and a four) therefore P(obtaining a four)* P(obtaining a ...
1
vote
2answers
36 views

(What is the formula to find) What is the probability that the sum of the numbers on the tickets chosen is at least 7?

Senario: Box A contains four equal-sized tickets, numbered 1, 2, 3 ,4 Box B contains three tickets of the same size, numbered 4, 5, 6 An experiment consists of selecting one ticket from the box A ...
1
vote
1answer
56 views

what is wrong in my answer and what will be the correct solution for this probability question ?

A and B play a game where each is asked to select a number from 1 to 5. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is - ...
0
votes
1answer
24 views

Probability “average” understanding

This is more of a problem understanding probabilities than an actual question. In a game I am playing I can use a certain item to try to unlock different levels. The item will unlock a new level ...
2
votes
0answers
40 views

Number of collisions of particles in a box. Application to epidemiology

I was surprised to see in this biology article a model assuming that the number of newly infected cells is a linear function of the number of (healthy) cells and of the number of viruses. I am not ...
0
votes
1answer
25 views

Calculating probabilities of events

Was going through past previous exam questions and came across this one: A manufacturer of lie detectors is testing its newest design. It asks 300 people to lie deliberately and another 500 people ...
0
votes
1answer
41 views

Two players $A,B$ throw two dice…

Two players $A,B$ throw two dice. A throw first, and they throw it in turns (i.e. $A,B,A,B,A...$). If $A$ gets sum of $10$ at the dice he wins, if $B$ gets $9$ - he wins. What is the probability ...
0
votes
1answer
38 views

Combinations with multiple kids

In a certain country, it has been found over many years that $55$% of the babies born there are males. For a family in that country with five children, what is the probability that (i) the two ...
1
vote
3answers
47 views

Permutations of numbers

Given the five digits $1,3,4,6,$ and $7$. In the following question, it should be understood that repition of a digit is not allowed. (i) How many three-digit numbers can be formed from the ...
0
votes
1answer
46 views

conditional probability Pc(B)

I am looking for the probability of Pc(B) where the event of B={no two people are born in the same month} and event C= {exactly three people were born in the summer of june, july august} and there are ...
1
vote
0answers
33 views

probability of an event question

Find the probability of the event B= { NO two people are born in the same month}. There are 9 people involved by the way. Is it 1/12 * 1/11 * 1/10 * 1/9 * 1/8 * 1/7 * 1/6 * 1/5 * 1/4 * 1/3 * 1/2 * 1/1 ...
2
votes
1answer
88 views

X,Y are independent RVs with known characteristic functions. Find P(X+Y=2).

X,Y are independent random variables with the following characteristic functions: $ \phi_X(\theta) = \frac{1}{4}e^{i\theta}+\frac{3}{4}e^{i2\theta} \\ \phi_Y(\theta) = ...
2
votes
1answer
112 views

Conditional probability: Why can't I make this assumption?

Here is the question :If we are told that among the 10 coins, at least three have landed on heads. What is the probability that there are at most five heads? In other words, P( at most five head | ...
0
votes
1answer
201 views

Is it possible to derive the CDF of $Z$?

Assume that $X_i$, $Y_k$, $i=0,\ldots,N$, $k=1,\ldots,K$ are non-negative independent non-identically distributed random variables. Let us define the random variable $Z$ as \begin{align} ...
2
votes
2answers
220 views

$k$ balls into $n$ bins: how to formally account for “time”

We throw balls into the bins until no bin is empty. What is the expected time until no bin is empty? The solution goes: Let $Y$ be the random variable that counts the time until no bin remains ...