a deck of cards contains 6 blue, 7 yellow cards, three red cards, and 5 green cards. what is the theoretical probability of drawing a blue card replacing it and drawing a yellow card?
With replacement:
P(BY)=P(B)*P(Y)=(6/21)*(7/21)=2/21
To find the theoretical probability of drawing a blue card, replacing it, and then drawing a yellow card, we need to know the total number of cards in the deck and the number of blue and yellow cards.
In this case, the total number of cards in the deck is:
6 blue cards + 7 yellow cards + 3 red cards + 5 green cards = 21 cards
The number of blue cards is 6 and the number of yellow cards is 7.
Since you are replacing the blue card after drawing it, the probability of drawing a blue card and then a yellow card would be the product of the probabilities of each event.
The probability of drawing a blue card (P(blue)) is:
Number of blue cards / Total number of cards = 6 / 21
The probability of drawing a yellow card (P(yellow)) is:
Number of yellow cards / Total number of cards = 7 / 21
To find the probability of both events happening, we multiply the two probabilities together:
P(blue and yellow) = P(blue) * P(yellow) = (6/21) * (7/21) = 42/441 = 2/21
So, the theoretical probability of drawing a blue card, replacing it, and then drawing a yellow card is 2/21.