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EXAMPLE 4

Weather.

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EXAMPLE 4

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  1. Weather The table shows the numbers of tropical cyclones that formed during the hurricane seasons from 1988 to 2004. Use the table to estimate (a) the probability that a future tropical cyclone is a hurricane and (b) the probability that a future tropical cyclone in the Northern Hemisphere is a hurricane. EXAMPLE 4 Find a conditional probability

  2. Number of hurricanes P(hurricane) = Total number of Cyclones 760 0.483 = 1575 P(hurricane Northern Hemisphere) Number of hurricanes in Northern Hemisphere = Total number of Cyclones in Northern Hemisphere 545 0.477 = 1142 EXAMPLE 4 Find a conditional probability SOLUTION

  3. Selecting Cards You randomly select two cards from a standard deck of 52 cards. What is the probability that the first card is not a heart and the second is a heart if (a) you replace the first card before selecting the second, and (b) you do not replace the first card? EXAMPLE 5 Comparing independent and dependent events SOLUTION Let Abe “the first card is not a heart” and Bbe “the second card is a heart.”

  4. If you replace the first card before selecting the second card, then Aand Bare independent events. So, the probability is: 13 3 39 P(A and B) = P(A) P(B) = 0.188 = 52 16 52 If you do not replace the first card before selecting the second card, then Aand Bare dependent events. So, the probability is: 13 13 39 P(A and B) = P(A) P(B A ) 0.191 = = 51 68 52 EXAMPLE 5 Comparing independent and dependent events

  5. What If? Use the information in Example 4 to find (a) the probability that a future tropical cyclone is a tropical storm and (b) the probability that a future tropical cyclone in the Southern Hemisphere is a tropical storm. a. 0.38 ANSWER ANSWER 0.46 for Examples 4 and 5 GUIDED PRACTICE

  6. 1 = 16 a. ANSWER A spade, then a club 13 = 204 ANSWER for Examples 4 and 5 GUIDED PRACTICE Find the probability of drawing the given cards from a standard deck of 52 cards (a) with replacement and (b) without replacement.

  7. 1 = 169 a. ANSWER 1 = 221 A jack, then another jack ANSWER for Examples 4 and 5 GUIDED PRACTICE Find the probability of drawing the given cards from a standard deck of 52 cards (a) with replacement and (b) without replacement.

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