25. Each morning Gataro does one of the following exercises: \( \quad \) cycling, jogging or weightlifting. He chooses the exercise to do by rolling a fair die. The faces of the die are numbered \( 1,1,2,3,4 \) and 5 . If the score is 2,3 or 5 , he goes for cycling. If the score is 1 , he goes for jogging. If the score is 4 , he goes for weightlifting. (a) Find the probability that: (i) on a given morning, hoes for cycling or weightlifting: (ii) on two consecutive mornings he goes for jogging.

In how many ways can the digits in the number \( 7,441,111 \) be arranged?

3. La probabilidad de que cierta clase de componente sobreviva a una prueba de choque es de 0.85. De los siguientes 15 componentes que se prueban calcule la probabilidad de que: a). sobrevivan 10 componentes. \( R=0.04489 \) b). no sobrevivan máximo 2 componentes. \( R=0.6042 \) c) calcule el promedio de componentes que sobreviven. \( R=12.75 \)

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

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: \( \begin{array}{ll}\text { a) A male under the age of } 30 . \\ \text { b) A female. } \\ \text { c) A male over the age of } 21 . \\ \text { d) A person not older than } 21 . \\ \text { e) A male given that this person is over } 30 \text { years. } \\ \text { f) A female or between } 21 \text { and } 30 . \\ \text { g) A male or a female. }\end{array} \)

What is the probability of rolling a 1 or a 4 on a number cube labeled 1 through 6 ? B. \( \frac{1}{6} \) D. \( \frac{1}{3} \) E. \( \frac{1}{2} \) E. \( \frac{5}{6} \)