How might we calculate the following cumulative probabilities? a. The outcome \( p \) happens \( n \) times in a row: b. The outcome \( p \) fails to occur \( n \) times in a row: c. The outcome \( p \) happens at least once in \( n \) attempts: d. The outcome \( p \) fails to occur at least once in \( n \) attempts:

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 - 5 females aged between 21 and 30 - 7 males over the age of 30 Calculate the probability that, if one person is selected at random from the group this person will be: \( \begin{array}{l}\text { a) A male under the age of } 30 . \\ \text { b) A female. } \\ \text { c) A male over the age of } 21 . \\ \text { d) A person not older than } 21 . \\ \text { e) A male given that this person is over } 30 \text { years. } \\ \text { f) A female or between } 21 \text { and } 30 . \\ \text { g) A male or a female. }\end{array} \)

Dalam almari A mmi terdapat beberapa helai baju kemeja-T. I helai berwarna puth, 4 helai berwama hitam, 3 helai berwarna merah dan 3 helai berwarna hijau. Dia memilih schelai baju kemeja-T secara rawak dan didapati kebarangkalian memilih baju hitam ialah \( \frac{2}{9} \). Hitung nilaix: In Azmi's wardrobe, there are few pieces of \( T \)-shirts, \( x \) white shirts, 4 black shirts, 3 red shirts and 3 green shirts. He chooses a \( T \)-shirt at random and the probability of him choosing the black shirt is \( \frac{2}{9} \). Calculate the value of \( x \). A 4 B 6 C 8 D 10

2.) Hannes wirft einen gewöhnlichen Spielwürfel. Wie groß ist die Wahrscheinlichkeit, dass die geworfene Augenzahl... \( \begin{array}{ll}\text {... kleiner als } 4 \text { ist? } & \text { B) ... eine gerade Zahl ist? }\end{array} \)

A bag contains green balls and red balls only. A ball is taken at random from the bag. The probability of taking a green ball is 0.38 . Write down the probability of taking a a red ball, b a blue ball.

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.