Question

For the following experiments list:

a) the possible events in the sample space; and b) the probability of each event.

EXAMPLE: one flip of a normal coin.

• Sample space: {heads, tails}
• Probabilities: P(heads) = .5, P(tails) = .5

1. A random draw from a bag containing 8 red balls and 5 green balls.
2. The simultaneous flip of two normal coins.
3. The flip of a coin and the roll of a normal 6-sided die.

Answer 1

A random draw from a bag containing 8 red balls and 5 green balls

Sample space = {red ball, green ball}

P[red ball] = 8/13 = 0.615. P[green ball] = 5/13 = 0.384

The simultaneous flip of two normal coins

H = Heads, T = Tails

Sample space = {HH, TT, HT(there is no TH as the toss is simultaneous)}

P[HH] = 1/3 = 0.33. P[TT] = 1/3 = 0.33. P[HT] = 1/3 = 0.33

The flip of a coin and the roll of a normal 6-sided die.

H = Heads, T = Tails, the number is the number on the dice

Sample space = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}

As all the events are equally probable, the probability of each event is = 1/12 = 0.08333