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8

A random variable X has the following probability distribution:

X | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

P(X) | 0 | k | 2k | 2k | 3k | K | 2 K | 7 K |

Determine

(i) k (ii) P(X < 3)

(iii) P(X > 6) (iv) P(0 < X < 3)

12

Suppose we have four boxes A, B, C and D containing coloured marbles as given below:

Box | Marble colour | ||

Red | White | Black | |

A | 1 | 6 | 3 |

B | 6 | 2 | 2 |

C | 8 | 1 | 1 |

D | 0 | 6 | 4 |

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?