In a group of people on holiday, it is established that there are: - 10 males under the age of 21 - 8 females under the age of 21 - 6 males aged between 21 and 30 - 5 females aged between 21 and 30 Calculate the probability that, if one person is selected at random from the group this person will be: \( \begin{array}{ll}\text { a) A male under the age of } 30 . \\ \text { b) A female. } \\ \text { c) A male over the age of } 21 . \\ \text { d) A person not older than } 21 . \\ \text { e) A male given that this person is over } 30 \text { years. } \\ \text { f) A female or between } 21 \text { and } 30 . \\ \text { g) A male or a female. }\end{array} \)

The events that Aaron's team and Betty's team win their next games are \[ \text { of } P(A) \text { and } P(B) \text {. } \] dependent equal product

4. A box contains a total of 100 CDs that were manufactured on two machines. Of them, 60 were manufactured on Machine I. Of the total CDs, 15 are defective. Of the 60 CDs that were manufactured on Machine I, 9 are defective. Let \( D \) be the event that a randomly selected CD is defective, and let A be the event that a randomly selected CD was manufactured on Machine I.

1. Según estadísticas la probabilidad de que el motor de un auto nuevo de cierta marca sufra algún desperfecto en el primer año de uso es de 0.02 , si se prueban tres automóviles de esta marca, encuentre el número esperado de autos que no sufren de algún desperfecto en el primer año y su desviación estándar. Resultados \( \mu=2.94 \) y \( \sigma=0.2425 \)

Jim works at an Auto centre and accidentally drops 4 bad spark plugs into a box with 20 good spark plugs. a. If he selects two spark plugs at random from the box without replacement, and the first spark plug selected was a good one, what is the probability that the second spark plug is bad?

11. One letter is selected from the word "ilovemathematics". What is the probability that a " \( t \) " or an " is chosen?