They are events and/or occurrences where the value and/or result of the previous similar event and/or occurrence does not affect the results obtained of the next event and/or occurrence.
For instance, when a die is rolled twice, the second roll is considered an independent event. This is so because the two rolls are separate incidences and the results of the second roll is only affected by the result of the first roll by such a minute amount that it is literally negligible.
Therefore, basically, Independent Events are just events that only has variables that directly affect it and not from a source that is linked to a previous random event. In other words, an event that is self-reliant.
Mini Task 4 *Proceed only if everything mentioned above is understood as the explanations will relate to above*
1(a) As mentioned earlier, a coin is relatively similar to a die, just that a coin has only 2 faces instead of the 6 faces on a die. Therefore, the event is an independent one.
(b) The event is the same as mentioned in the explanation above, just that a second die is added, thus, it still remains as an independent variable itself.
(c) This is a dependent variable as the probability of getting a king on the 3rd draw after the 2 aces , which were removed, is increased as compared to getting a king on the first draw since the number of total cards are reduced by 2, which increases the possibility of getting any card in the deck except for aces. Thus, the event is a dependent one.
(d) The explanation is somewhat similar to that is (c), where in order to have an increased chance of picking a white ball, the number of the red balls, which is the only other possible type of balls picked, should be reduced. In this case, the event fits the requirement of an increased chance in getting a white ball picked on the second draw. Thus, it is a dependent event.
A coin only has two faces, heads and tails. Since there are only 3 coins and the probability to be calculated is having all 3 coins to have heads, we just take the number of possibilities and multiply it by itself the number of times the number of coins there are, which would give us a sample space of 8 different results. Since getting a heads, heads, heads is only possible in one scenario, we will be able to obtain the probability of 1/8.
Mini Task 5