Question

Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.Drawing three fives in a row from a standard deck of cards when the drawn card is not returned to the deck each timeQuestion content area bottomPart 1The event of drawing a and the event of drawing a the next time are▼

Answer 1

Answer:(a) dependent events (b) P(all three cards 5 ) = 1/5525

Explanation :

Part (a)

• We are told that cards are drawn without replacement , meaning the drawing of one card at a time will affect the occurence of the other card .

,

• Therefore , ,these events are dependent

Part (b)

• Take note that the deck of cards has 52 cards

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• There are 4 cards of number 5 in the deck out of 52 cards

• Probability of first card to be a 5 , is represented as

P (first card 5) = 4/52 , then

P( second card 5 ) = 3/51 , and

P(third card 5 ) = 2/50

So, the probability of drawing three fives in a row from a standard deck of cards when the drawn card is not returned to the deck each time will be :

`\begin{gathered} P(\text{ all three cards that are 5 \rparen = }(4)/(52)*(3)/(51)*(2)/(50) \\ \text{ =}(1)/(5525) \\ \text{ } \end{gathered}`

Therefore , P(all three cards 5 ) = 1/5525