Dependent Events In Probability: Examples And Calculations

Dependent Events

2 events in which the occurrence of one event does affect the occurrence of the other event

Dependent events refer to events where the outcome of one event affects the outcome of the subsequent event. In other words, the probability of the second event occurring depends on the occurrence of the first event. The two events are said to be dependent because the outcome of the first event affects the probability of the second event.

Examples of dependent events could include:

1. Drawing cards from a deck without replacement: If you draw a card and do not replace it, the probability of drawing another card will depend on the first card you drew.

2. Choosing socks from a drawer: If you have socks in a drawer and you randomly select one, the probability of selecting another sock of the same color will be dependent on the first sock selected.

3. Rolling dice: If you roll two dice, the probability of getting a certain number on the second roll will depend on the number that was rolled on the first roll.

The probability of two dependent events occurring together can be calculated using conditional probability. This involves multiplying the probability of the first event by the probability of the second event given that the first event has occurred.

For example, if you have a bag with 4 red balls and 6 white balls, and you draw one ball at random and do not replace it, the probability of drawing another red ball would be dependent on the first ball drawn. Therefore, the probability of drawing two red balls in a row would be:

P(RR) = P(Red on first draw) × P(Red on second draw given that the first ball was red)

= (4/10) x (3/9)

= 2/15

Therefore, the probability of drawing two red balls in a row is 2/15.

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