Question

Write the appropriate probability distribution formula in terms of x only and substitute in all the known parameters for each scenario.

a) The result when you roll a single fair octahedral die numbered 1 to 8.

b) counting the number of RED FACE CARDS in a three card hand dealt from a well shuffled deck.

c)counting the number of times you roll a prime number out of ten rolls of a single fair octahedral die.

Answer 1

A = number of black cards
B = number of picture cards (or face cards)
C = number of black picture cards

There are 26 black cards (spades and clubs), so A = 26.

There are 3 picture cards (Jack, Queen, King) in each suit. There are 4 suits (clubs, hearts, spades, diamonds). So there are 3*4 = 12 picture cards. This means B = 12

There are 2 suits which are black (spades and clubs) with 3 face cards per suit, so 2*3 = 6 cards which are both black cards and face cards. So C = 6

The number of cards that are either black cards or a face card, or both, is...

D = A+B-C
D = 26+12-6


D = 32