12.4 Multiplying Probabilities, II Dependent Events

Probability of 2 Dependent Events If two events, A and B, are dependent, then the probability of both events occurring is 𝑃 𝐴 𝑎𝑛𝑑 𝐵 =𝑃 𝐴 ∗𝑃(𝐵 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝐴) Recall: Independent events – current choices affect future choices.

Example – Two Dependent Events The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability. A vacation, then a car. A – B – 𝑃 𝐴 = 𝑃 𝐵 = 𝑃 𝐴 𝑎𝑛𝑑 𝐵 =

Example – Two Dependent Events The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability. A vacation, then a car. A – first selection is vacation B – second selection is car 𝑃 𝐴 𝑃 𝐵 = 𝑃 𝐴 𝑎𝑛𝑑 𝐵 =

Example – Two Dependent Events The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability. A vacation, then a car. A – first selection is vacation B – second selection is car 𝑃 𝐴 =3/10 𝑃 𝐵 = 𝑃 𝐴 𝑎𝑛𝑑 𝐵 =

Example – Two Dependent Events The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability. A vacation, then a car. A – first selection is vacation B – second selection is car 𝑃 𝐴 =3/10 𝑃 𝐵 =1/9 𝑃 𝐴 𝑎𝑛𝑑 𝐵 =

Example – Two Dependent Events The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability. A vacation, then a car. A – first selection is vacation B – second selection is car 𝑃 𝐴 =3/10 𝑃 𝐵 =1/9 𝑃 𝐴 𝑎𝑛𝑑 𝐵 = 3 10 1 9 = 1 30

Example 2– Two Dependent Events The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability. Two televisions. A – B – 𝑃 𝐴 = 𝑃 𝐵 = 𝑃 𝐴 𝑎𝑛𝑑 𝐵 =

Example 2– Two Dependent Events The host of a game show is drawing chips from a bag to determine the prizes for which contestants will play. Of the 10 chips in the bag, 6 show televisions, 3 show vacation, and 1 shows car. If the host draws the chips at random and does not replace them, find each probability. Two televisions. A – first selection is television B – second selection is television 𝑃 𝐴 =6/10 𝑃 𝐵 =5/9 𝑃 𝐴 𝑎𝑛𝑑 𝐵 = 6 10 5 9 = 1 3

Example Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order. A – B – C –

Example Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order. A – First card is diamond B – Second card is club C – Third card is diamond

Example Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order. A – First card is diamond B – Second card is club C – Third card is diamond

Example Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order. A – First card is diamond B – Second card is club C – Third card is diamond

Example Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order. A – First card is diamond B – Second card is club C – Third card is diamond

Example Three cards are drawn from a standard deck of cards without replacement. Find the probability of drawing a diamond, a club, and another diamond in that order. A – First card is diamond B – Second card is club C – Third card is diamond

Assignment

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