Independent And Dependent Events Day 2

The probability of selecting a girl and then a boy with replacement can be found by multiplying the probability of selecting a girl (14/26) by the probability of selecting a boy (12/26). This can be simplified to (14/26) * (12/26) = 168/676 = 42/169.

The probability of selecting a boy on the first draw is 12/26. After the first boy is selected, there are 11 boys left out of a total of 25 students. Therefore, the probability of selecting another boy on the second draw without replacement is 11/25. Multiplying these probabilities together gives (12/26) * (11/25) = 132/650, which simplifies to 66/325.

The probability of drawing an Ace from a standard deck of 52 cards is 4/52, since there are 4 Aces in the deck. After replacing the card, the probability of drawing a Jack is also 4/52. To find the probability of both events happening, we multiply the probabilities together: (4/52) * (4/52) = 16/2704 = 1/169. Therefore, the correct answer is 1/169.

The probability of rolling a 5 on a standard die is 1/6, and the probability of flipping a tail on a coin is 1/2. Since the events of rolling a 5 and flipping a tail are independent, we can multiply the probabilities together to find the probability of both events occurring. Therefore, the probability of rolling a 5 and then flipping a tail is (1/6) * (1/2) = 1/12.

The probability of drawing a King from a standard deck of 52 cards is 4/52 since there are 4 Kings in the deck. After drawing the first King, there are only 51 cards left in the deck, and 3 Kings remaining. Therefore, the probability of drawing another King without replacement is 3/51. To find the probability of both events happening, we multiply the probabilities together: (4/52) * (3/51) = 1/221.