Alex and bob are playing 5 chess games. alex is 3 times more likely to win than bob. what is the probability that both of them will win at least 2 games?

12.2%

Step-by-step explanation:

Lets firstly find out the probabilities for Alex and Bob. We know that the prb that Alex wins is 3 times the prob for Bob, so:

P(A) = 3P(B)

And, as these values are probabilities they must sum 1:

P(A) + P(B) = 1

Replacing the first equation in the second:

3P(B) + P(B) = 1

4P(B) = 1

Dividing both sided by 4:

4P(B)/4 = 1/4

P(B) =1/4

So, the probability for Bob is 1/4. Then the probability for Alex is 3*1/4 = 3/4

Now we have to find the probability that both win at least two games. Lets think about the possible combination of cases. As they play 5 games and both have to win at least to there is a remaining game that cane variate, this is, can be won by Alex or Bob. So, we can have:

AABBB

AABBA

Where A is "Alex win" and B is "Bob win" (here we do not pay attention to the order).

Thus, we have to find the probability that Alex wins 3 games and Bob 2 games, and the probability that Alex wins 2 games and Bob 3 games. As the games are independent, i.e., the result of one games does not affect the followings we can just multiply the probabilities:

P(3A and 2B) = (3/4)*(3/4)*(3/4)*(1/4)*(1/4) = 0.42*0.06 = 0.026

P(2A and 3B) = (3/4)*(3/4)*(1/4)*(1/4)*(1/4) = 0.56*0.016 = 0.096

So,

P (at least 2) = P(3A and 2B) + P(2A and 3B) = 0.026 + 0.096 = 0.122 = 12.2%

the answer is 175.4379

step-by-step explanation:

the cat is blue because the probability of extension towards the prefix of the diameter of the circle could only mathematically equal to the sum of the roots of the carrots from   your garden.

step-by-step explanation: