Please help and please show your work 2 Three cards are rand

Please help and please show your work

2. Three cards are randomly selected, without replacement, from an ordinary deck of 52 playing cards. (a) Compute the probability that the first card selected is a spade. (b) Compute the probability that the second card selected is a spade. (c) Compute the conditional probability that the first card selected is a spade, given that the second and third cards are spades. (Compare your answer in part (a) with your answer in part (c). Does it seem reasonable?)

Solution

1)

first card is spade

P= (first spade)(second any card)(thrid any card)

= 13/52 *51/51 * 50/50

= 1/4

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2)

second card is spade

P= (first spade)(second spade)(thrid any card) + (first not spade)(second spade)(thrid any card)

= 13/52 *12/51 * 50/50 + 39/52 *13/51 * 50/50

= 1/4

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3)

P1= (first spade)(second spade)(thrid spade) + (first not spade)(second spade)(thrid spade)

= 13/52 * 12/51*11/50 + 39/52*13/51*12/50

= 1/17

P2 = (first spade)(second spade)(thrid spade)

= 13/52 * 12/51*11/50

= 11/850

so req probability = P(first spade) / P(second and third spade)

= P(all three spade) / P(second and third spade)

= P2/P1

= (11/850)/(1/17)

= 11/50

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DONE PLEASE RATE ....ASK IF ANY DOUBT